Former Massachusetts Gov. Mitt Romney and Rep. Ron Paul, R-Texas, run neck-and-neck with President Obama in a general-election matchup, according to a new CBS News poll released late on Monday that shows the two front-runners in Tuesday's New Hampshire GOP primary running stronger against the president than their fellow Republicans.
Romney posts a two-point lead over Obama, 47 percent to 45 percent, within the poll's margin of error of plus or minus 2.8 percentage points. He leads Obama, 45 percent to 39 percent, among independent voters.
Obama's lead over Paul is just one point, 46 percent to 45 percent, as Paul leads among independents by 7 points.
The president posts more significant leads over the other GOP candidates, but against each he is below the critical 50-percent threshold: He leads former House Speaker Newt Gingrich, 49 percent to 41 percent; former Utah Gov. Jon Huntsman, 48 percent to 41 percent; Texas Gov. Rick Perry, 49 percent to 42 percent; and former Sen. Rick Santorum, R-Pa., 47 percent to 43 percent.
Among all adults, just 45 percent of Americans approve of the job Obama is doing as president, slightly worse than the 47-percent approval rating he posted last month. Among independents, 38 percent approve of Obama's job performance, while 49 percent disapprove.
Results released earlier Monday among Republicans who said they intend to vote in their state's presidential nominating contest showed Romney running slightly ahead of the rest of the field, but nearly a third of Republicans are undecided or seeking a candidate not currently in the race.
The CBS News poll was conducted Jan. 4-8, surveying 1,413 adults, for a margin of error of plus or minus 2.6 percentage points. The poll includes a subsample of 1.247 registered voters.
Photos and video from New Hampshire:
Republican presidential candidate, Rep. Ron Paul, R-Texas, speaks to supporters during an election night really in Manchester, N.H., Tuesday, Jan. 10, 2012. (AP Photo/Bill Sikes)
Republican presidential candidate, Rep. Ron Paul, R-Texas, and his wife Carol greet supporters as they take the stage during an election night really in Manchester, N.H., Tuesday, Jan. 10, 2012. (AP Photo/Stephan Savoia)
A supporter of Republican presidential candidate House Speaker Newt Gingrich reacts to the news his candidate is loosing the New Hampshire presidential primary at Gingrich's rally headquarters Tuesday, Jan. 10, 2012, in Manchester, N.H. (AP Photo/Jim Cole)
Republican presidential candidate, former Utah Gov. Jon Huntsman shakes hands with supporters during a New Hampshire Primary night party in Manchester, N.H., Tuesday Jan. 10, 2012. Hunstman finished third, behind Ron Paul and Mitt Romney, who won the Granite State primary. (AP Photo/Charles Krupa)
Republican presidential candidate, former Utah Gov. Jon Huntsman and his wife Mary Kaye arrive for a New Hampshire primary night party in Manchester, N.H., Tuesday Jan. 10, 2012. Huntsman is projected to finish third, behind Mitt Romney, who came in first, and Ron Paul, who was projected to finish second. (AP Photo/Charles Krupa)
Former Massachusetts Gov. Mitt Romney waves to supporters at the Romney for President New Hampshire primary night victory party at Southern New Hampshire University in Manchester, N.H., Tuesday, Jan. 10, 2012. (AP Photo/Elise Amendola) (AP Photo/Elise Amendola)
Former Massachusetts Gov. Mitt Romney surrounded by his family points towards supporters at the Romney for President New Hampshire primary night victory party at Southern New Hampshire University in Manchester, N.H., Tuesday, Jan. 10, 2012. (AP Photo/Elise Amendola) (AP Photo/Elise Amendola)
Republican presidential candidate, former Massachusetts Gov. Mitt Romney, celebrates at his New Hampshire primary election party in Manchester, N.H., Tuesday, Jan. 10, 2012. (AP Photo/Charles Dharapak)
Supporters of Republican presidential candidate, former Massachusetts Gov. Mitt Romney, react as it was declared that he was the winner of the New Hampshire Primary Election at his reception in Manchester, N.H., Tuesday, Jan. 10, 2012. (AP Photo/Charles Dharapak)
Rep. Ron Paul, R-Texas supporter, Melina Brajovic calls out to voters driving into a polling station, Tuesday, Jan. 10, 2012, during the first-in-the-nation presidential primary, at Hilltop Middle School in Manchester, N.H. (AP Photo/Matt Rourke)
A voter casts their ballot on primary election day at the Webster School polling location in Manchester, New Hampshire on January 10, 2012. UPI/Kevin Dietsch (UPI/Kevin Dietsch)
Republican presidential candidate, former Utah Gov. Jon Huntsman, makes it pass a crush of reporters as he campaigns on primary election day outside of a polling station at Webster School in Manchester, N.H., Tuesday, Jan. 10, 2012. (AP Photo/Charles Dharapak) (AP Photo/Charles Dharapak)
Republican presidential candidate, former Utah Gov. Jon Huntsman speaks at a campaign rally in Exeter, N.H. Monday, Jan. 9, 2012. (AP Photo/Elise Amendola) (AP Photo/Elise Amendola)
Republican presidential candidate, former Utah Gov. Jon Huntsman arrives at the Webster School in Manchester, N.H., Tuesday, Jan. 10, 2012, where primary voting was taking place. (AP Photo/Evan Vucci) (AP Photo/Evan Vucci)
Republican presidential candidate, former Massachusetts Gov. Mitt Romney, gives a thumbs up as he campaigns on primary election day outside of a polling station at Webster School in Manchester, N.H., Tuesday, Jan. 10, 2012. (AP Photo/Charles Dharapak) (AP Photo/Charles Dharapak)
Republican presidential candidate, former Massachusetts Gov. Mitt Romney carries a young girl as he campaigns on primary election day outside of a polling station at Webster School in Manchester, N.H., Tuesday, Jan. 10, 2012. (AP Photo/Charles Dharapak) (AP Photo/Charles Dharapak)
Republican presidential candidate, former Massachusetts Gov. Mitt Romney, campaigns on primary election day outside of a polling station at Webster School in Manchester, N.H., Tuesday, Jan. 10, 2012. (AP Photo/Charles Dharapak) (AP Photo/Charles Dharapak)
Republican presidential candidate, former House speaker Newt Gingrich is surrounded by media outside the Webster School in Manchester, N.H., Tuesday, Jan. 10, 2012, where primary voting was taking place. (AP Photo/Evan Vucci) (AP Photo/Evan Vucci)
Republican presidential candidate, former House Speaker Newt Gingrich, obscured right, walks behind his wife Callista through a group of reporters as he campaigns on primary election day outside of a polling station at Webster School in Manchester, N.H., Tuesday, Jan. 10, 2012. (AP Photo/Charles Dharapak) (AP Photo/Charles Dharapak)
Republican presidential candidate, Rep. Ron Paul, R-Texas, campaigns on primary election day outside of a polling station at Webster School in Manchester, N.H., Tuesday, Jan. 10, 2012. (AP Photo/Charles Dharapak) (AP Photo/Charles Dharapak)
Republican presidential candidate, Rep. Ron Paul, R-Texas, answers a question during a meet and greet at the Hollis Community Center in Hollis, N.H., Monday, Jan. 9, 2012. (AP Photo/Stephan Savoia)
Republican presidential candidate, Rep. Ron Paul, R-Texas waits to be introduced before speaking to the employees of Timberland, LLC in Stratham, N.H., Monday, Jan. 9, 2012. (AP Photo/Stephan Savoia)
Republican presidential candidate, former Pennsylvania Sen. Rick Santorum visits Mary Ann's Diner, Monday, Jan. 9, 2012, in Derry, N.H. (AP Photo/Evan Vucci)
Republican presidential candidate, former Pennsylvania Sen. Rick Santorum speaks at a town hall meeting on the soccer field at Rivier College, Monday, Jan. 9, 2012, in Nashua, N.H. (AP Photo/Evan Vucci)
Republican presidential candidate former Pennsylvania Sen. Rick Santorum speaks during a campaign rally Monday, Jan. 9, 2012, in Manchester, N.H. (AP Photo/Evan Vucci)
Rick Santorum campaigns with New Hampshire supporters ahead of Tuesday's primary. (Liz Lynch)
Tom Tillotson removes ballots for counting that were cast after midnight in the first-in-the-nation presidential primary, at the Balsams Grand Resort, Tuesday, Jan. 10, 2012, in Dixville, N.H.
Republican presidential candidate Mitt Romney campaigns at McKelvie Intermediate School in Bedford, N.H., on Monday. (AP Photo/Charles Dharapak)
Newt Gingrich's campaign bus is parked outside during a beautiful day in Nashua. Maybe the sky is the limit for Gingrich's campaign. (Liz Lynch)
Mitt Romney speaks to a crowd of supporters in Manchester on Sunday, Jan. 8. (Liz Lynch)
Supporters of Republican candidates stand outside in Manchester on Saturday, Jan. 7. (Liz Lynch)
Republican presidential candidate Jon Huntsman stands on a counter during a campaign stop at the Bean Towne Coffee House on Sunday, Jan. 8 in Hampstead. (AP Photo/Evan Vucci)
GOP presidential candidate Mitt Romney campaigns at the Rochester Opera House on Sunday, Jan. 8. (AP Photo/Charles Dharapak)
Newt Gingrich kisses his wife, Callista, after a debate at the Capitol Center for the Arts in Concord on Sunday, Jan. 8. (AP Photo/Charles Krupa)
Mitt Romney reacts as he walks off the stage after a debate at the Capitol Center for the Arts in Concord on Sunday, Jan. 8. (AP Photo/Charles Krupa)
Rick Santorum (center) walks of the stage after the debate at the Capitol Center for the Arts on Sunday, Jan. 8. Rivals Mitt Romney, (left) and Ron Paul are in the background. (AP Photo/Charles Krupa)
Rick Perry answers a question as Newt Gingrich listens during the debate at the Capitol Center for the Arts in Concord on Sunday, Jan. 8. (AP Photo/Charles Krupa)
Rick Santorum reacts as Mitt Romney answers a question during the debate at the Capitol Center for the Arts in Concord on Sunday, Jan. 8. (AP Photo/Charles Krupa)
Jon Huntsman, Rick Santorum, Mitt Romney, Ron Paul, Newt Gingrich, and Rick Perry are introduced before a candidate debate at the Capitol Center for the Arts in Concord on Sunday Jan. 8. (AP Photo/Charles Krupa)
Charles Badger of Washington, a supporter of Mitt Romney, demonstrates outside the Chubb Theater before the debate on Sunday, Jan. 8,in Concord. (AP Photo/Matt Rourke)
Mitt Romney points toward the audience as Rick Santorum looks on before the debate at the Capitol Center for the Arts in Concord on Sunday, Jan. 8. (AP Photo/Charles Krupa)
Peter Romersa (left) of Stamford, Conn., protests with others outside the debate at the Chubb Theater on Sunday, Jan. 8 in Concord, N.H. (AP Photo/Matt Rourke)
Rick Santorum says that Mitt Romney shouldn't call anyone "middle class" - middle income maybe, but the former term implies "class warfare." [SarahB_CBSNJ via Twitter] (Elise Amendola/AP)
Mitt Romney says he would bring home U.S. troops from Afghanistan as soon as he can by going there and listening to the commanders on the ground. [SarahB_CBSNJ via Twitter] (Elise Amendola/AP)
Newt Gingrich rails against the media for not covering "anti-Christian bigotry" at Saint Anselm College in Manchester, N.H. [Rebecca_CBSNJ via Twitter] (Elise Amendola/AP)
Mitt Romney encourages same-sex couples to build a life together but says he doesn't support gay marriage. [@Roarty_NJ via Twitter] (Elise Amendola/AP)
At the debate on Saturday night, Ron Paul says, "How many times have you seen a white, rich person get the electric chair?" [@ethanklapper via Twitter] (Elise Amendola/AP)
Jon Huntsman comes out in favor of civil unions, saying he doesn't feel that they threaten his marriage. [@Rebecca_CBSNJ via Twitter] (Elise Amendola/AP)
Rick Perry calls for sending troops back into Iraq. [@Rebecca_CBSNJ via Twitter] (Elise Amendola/AP)
Jon Huntsman (left) and Mitt Romney (right) listen to Ron Paul answer a question during a debate. (Elise Amendola/AP)
Mitt Romney at a rally on Saturday morning in Derry, N.H. (Allen Gannett)
Rick Santorum at a rally on Saturday afternoon in Hollis, N.H. (Allen Gannett)
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