(CBS) -- On the day President Obama and Mitt Romney will face off in their first debate, a new round of polling shows a tight race nationally and a more competitive race in a couple key swing states.
A new Quinnipiac survey of likely voters nationwide shows Mr. Obama leading Romney, 49 percent to 45 percent. That puts the president slightly within of the poll's margin of error, which is +/- 2.2 percent. Mr. Obama's lead can be attributed in part to his 18-point lead among women.
Voters' slight preference for Mr. Obama may give Romney the advantage of going into the debate facing lower expectations -- 54 percent said they expected the president to win the debates, while 28 percent expected Romney to. Likely voters are split over who would do a better job handling the economy, with 48 percent naming Mr. Obama and 47 percent saying Romney would.
A National Journal nationwide poll shows the candidates on even footing, with 47 percent support each among likely voters.
A poll released Tuesday by NBC and the Wall Street Journal also shows a very close race: Mr. Obama leads Romney among likely voters nationally, 49 percent to 46 percent -- within the poll's 3.4 percent margin of error.
This poll similarly shows Mr. Obama with a solid lead among women, as well as among Hispanics. As many as 71 percent of likely Hispanic voters say they support him. The president also benefits from the fact that just 13 percent say the economy will get worse in the next four years -- the lowest number since Mr. Obama took office. And while a majority of Americans think the country is on the wrong track, 57 percent say the economy is improving.
A trio of NBC/WSJ polls in key states also show Romney gaining some ground. In Virginia, Mr. Obama leads 48 percent to 46 percent. In Florida, Mr. Obama leads 47 percent to 46 percent. In a September NBC/WSJ survey, Mr. Obama led in both states by five points.
However, Mr. Obama still holds a solid eight-point lead among likely voters in Ohio (51 percent to 43 percent).
A Suffolk University poll also shows Mr. Obama leading by just three points among likely voters Florida -- within the poll's four-point margin of error. Mr. Obama takes 46 percent to Romney's 43 percent, while 7 percent remain undecided.
Fifty-two percent of likely voters in this survey expect Mr. Obama to win tonight's debate, while 19 percent say Romney will.