Nationally, 48 percent of likely voters surveyed said they supported Democrat Obama and 46 percent backed Romney, a former Massachusetts governor, polling showed.
In swing states, Obama maintained a 4-percentage point lead in Ohio and was ahead by slimmer margins in Virginia and Colorado, while Romney led by 1 percentage point in Florida.
The electoral college system and the way the state polls are going suggests that Obama could be headed toward re-election partly due to his lead in Ohio, Ipsos pollster Julia Clark said.
Both candidates made their final urgent pleas to voters on Monday in a closing sprint through battleground states, hoping to whip up strong turnout from supporters and to sway the few remaining undecided voters.
In likely the most important swing state of Ohio, Obama had support of 50 percent, while Romney was at 46 percent.
In Virginia, Obama held a slim lead of 48 percent to Romney's 46 percent and in Colorado, the Democrat was also at 48 percent, a nose ahead of Romney's 47 percent.
Romney, however, had a slight lead in the most populous swing state Florida, where 48 percent of likely voters sided with the Republican and 47 percent backed Obama.
A victory in US presidential elections relies not on a popular vote count but reaching 270 electoral college votes, which are given to each state based on population size.
"Obama only needs a couple of these swing states," Clark said, "and the data suggests that he'll win one or two of them."
All of the polls' results are within the polls' credibility intervals, a tool used to account for statistical variation in Internet-based polling. Nationally, the credibility interval for likely voters was plus or minus 3.4 percentage points.