President Obama holds a slight four-point lead over Mitt Romney among those likeliest to vote in the crucial swing state of Ohio, a CNN/ORC poll released Tuesday shows -- an advantage that is slimmer than polls showed the incumbent holding in the Buckeye State before last week’s debate.

Obama leads Romney 51 percent to 47 percent in the poll of likely voters, with one-in-eight saying they could change their mind before Election Day. Among registered voters, Obama's lead is 10 points, 53 percent to 43 percent. Obama holds a wide advantage among women (60-38) while Romney leads comfortably among men (56-42). Independents are evenly divided, with 50 percent going for Obama and 46 percent choosing Romney.

An NBC/Wall Street Journal/Marist poll conducted several days before last Wednesday's debate showed Obama leading Romney in Ohio 51 percent to 43 percent. (NBC/Marist/WSJ is set to release more polling in Ohio -- as well as Virginia and Florida -- Thursday morning.) Late September polls from the Washington Post and the Columbus Dispatch showed Obama leading by comparable margins in the Buckeye State.

The Ohio poll is among the first live-caller, non-partisan surveys of a swing-state to be released in the aftermath of last week’s debate, which was widely viewed as a victory for Romney. The poll was conducted Friday through Monday. 

In national surveys, Romney also appears to have enjoyed a post-debate bump. A Pew Research Center poll released Monday showed Romney jumping out to a four-point lead among likely voters after trailing Obama by eight points in mid-September and Gallup's lastest tracking poll puts the race at Romney 49 percent Obama 47 percent among likely voters.

No Republican has ever won the presidency without carrying Ohio, a prize which brings with it 18 electoral votes this year. Both Obama and Romney are in the state on Tuesday – the deadline to register to vote there. Romney is enlisting the help of New Jersey Gov. Chris Christie, who will stump with him in the state on Wednesday as well.