Washington (CNN) - A new national poll in the battle for the GOP presidential nomination conducted entirely after last week's CNN/Tea Party Republican debate indicates that Texas Gov. Rick Perry remains at the top of the pack. But according to the USA Today/Gallup survey, Perry doesn't fare as well as former Massachusetts Gov. Mitt Romney in hypothetical 2012 general election matchups against President Barack Obama.
The poll indicates that 31 percent of Republicans and independents who lean toward the GOP say they support Perry for their party's presidential nomination, with 24 percent backing Romney, who's making his second bid for the White House.
Thirteen percent support Rep. Ron Paul of Texas, who's making his third run for the presidency, with Rep. Michele Bachmann of Minnesota, businessman, former Godfather's Pizza CEO and radio talk show host Herman Cain, and former House Speaker Newt Gingrich all at five percent. Everyone else registered in the low single digits.
The poll, released Monday evening, was conducted Thursday through Sunday, after last Monday's debate in Tampa, Florida.
The survey suggests that Perry is stronger with Republicans and independents who lean toward the GOP, the voters who will decide the Republican presidential nomination, while Romney does better among swing voters who could be very influential in deciding next year's general election.
In hypothetical general election matchups, Romney holds a two point margin over Obama, 49 to 47 percent, while the president holds a five point advantage over Perry, 50 to 45 percent. Both margins are within the poll's sampling error.
The GOP White House hopefuls meet again on the same stage this Thursday, at a debate in Orlando, Florida. The Fox/Republican Party of Florida showdown is the third presidential debate since Labor Day.
The USA Today/Gallup poll was conducted September 15-18, with 889 registered voters questioned by telephone. The survey's overall sampling error is plus or minus four percentage points.
– Follow Paul Steinhauser on Twitter: @PSteinhauserCNN.