"At least he could likely deliver Ohio," said one Republican.
Among Republicans, the next most popular pick was Sen. Marco Rubio, R-Fla., with 21 percent support, followed by Rep. Paul Ryan, R-Wis., (17 percent), and Sen. Kelly Ayotte, R-N.H., (8 percent). Sen. John Thune, R-S.D., received no votes among either Democrats or Republican lawmakers.
After Portman, Democrats ranked Ryan, Rubio and Ayotte in order as the best picks.
"Portman conveys seriousness of purpose," one Democrat said. "The rest are political supernovas who will fade away fast."
Another Democrat conceded that Portman would "be a solid, well-vetted candidate who is also a family man who can sell to Middle America."
Portman, who spent more than a decade in the House and worked in both Bush administrations, "understands how to make the executive branch run. He could turn the VP position from a cipher into a [chief operating officer] for government," said one Republican.
Democrats are hoping to make Ryan's Medicare proposal a central issue this year. And some suggested they'd welcome him to the ticket - as a boon for Democrats. "Why not put the architect of the effort to repeal Medicare on the ticket to defend that move personally?" one Democrat said.
Among the GOP boosters of Ryan, the House Budget Committee chairman, one Republican said, "If Romney wants the election to be economy and spending, put your best man on the field."
Or Romney could put a women on the field, another Republican suggested, pitching Ayotte. "White women are the most important demographic in this election. She is new to the national scene, but she is smart, tough, poised, knows how to 'make a case,' and offers Romney cross-generational appeal. It would mean taking a risk, but one that reflects well on Romney."
Lawmakers were more split over what type of politician - a member of Congress, a governor or a former officeholder - Romney should tap as vice president. A plurality of Republicans (39 percent) said he should pick a governor, but nearly a quarter volunteered another answer.
"What matters is the person's credibility on jobs, not their current job," said one Republican.
But relationships on the Hill matter, chimed in another Republican. "Politically, a governor or former officeholder would probably be best right now, but Mitt Romney needs someone he can trust who will work the Hill. Ask any member, and they'll tell you Obama failed miserably at the task."
Democrats preferred a member of Congress (37 percent), though a quarter volunteered another answer, with many saying the profession of Romney's pick wouldn't matter much. "Any of the above. It's who, not what," one Democrat said.