Both polls were conducted after Tuesday night, when Mourdock's answer to a debate question about abortion went viral and brought national attention to the Indiana race.
"I think even when life begins in that horrible situation of rape, that it is something that God intended to happen," Mourdock said at the debate.
The DSCC poll found that 76 percent of likely Indiana voters have "seen or heard about comments U.S. Senate candidate Richard Mourdock made in a recent debate that when a woman gets pregnant from rape it is something that God intended."
Mourdock, who upset Sen. Richard Lugar in the GOP primary earlier this year, was initially expected to win in the solidly red state. But Donnelly and his allies have kept the race close by portraying the state Treasurer as an extremist while touting Donnelly as a moderate.
The Mourdock poll was conducted Wednesday and Thursday by McLaughlin & Associates. The survey of 600 likely voters has a margin of error of plus-or-minus 4 percentage points.
The DSCC poll, conducted over the same time period by Anzalone Liszt Research, surveyed 446 likely voters, for a margin of error of plus-or-minus 4.6 percentage points.