By Jean-Paul Salamanca (staff@latinospost.com) | First Posted: Nov 05, 2012 01:42 PM EST

President Barack Obama is holding on slightly to two critical swing states, Ohio and Virginia, but new polls released Sunday show that the race could be closer than that.

Real Clear Politics polls on Nov. 4 show Obama ahead of Romney in Ohio-arguably the most important of the eight swing states-49.6 percent to 46.8 percent. This comes on the heels of three new polls released on Sunday.

The first, from Republican-leaning Rasmussen Reports, shows a tie between Obama and Romney at 49 percent in a poll of 750 likely voters, with a margin of error of 4.0 percent.

As to why the race is so close in their polls, Rasmussen writes that they ask Ohio voters which candidate they trust more in several key policy areas.

"Romney has a three-point edge over the president in voter trust when it comes to the economy, a two-point lead in the area of job creation and is ahead by one point with regards to energy policy. But Ohio voters trust Obama more by four points when it comes to housing issues and by two points in the area of national security," Rasmussen reported.

A second one from the University of Cincinnati shows Obama leading 50 percent to 49 percent; that poll of 901 likely voters has a 3.3 percent error margin. And a third one from Public Policy Polling projected Obama ahead of Romney 52 percent to 47 percent among 1,000 likely voters.

In Ohio Obama's already built up a large lead during the early voting period," Public Policy Polling writes. "He's up 60/39 with those who already cast their ballots. Romney's ahead 51/48 with people who plan to vote on Election Day but he's going to need a much wider margin than that to take the state."

Meanwhile, in Virginia, the polls are much closer in a state that Obama won by 6.3 points in 2008. Real Clear Politics shows Obama with a tiny 0.3 lead ahead of Romney in the polls, 48.0 percent to 47.7 percent. This reflects the recent updated data from two polls, Rasmussen and Public Policy Polling.

Rasmussen polls of 750 likely voters project Romney holding a two-point edge in the state, leading 50 percent to 48 percent.

"Romney has the support of 90% of Virginia Republicans and leads 58% to 37% among voters not affiliated with either of the major parties," the polling firm writes. "The president has 93% backing from the state's Democrats."

Meanwhile, Public Policy Polling is showing a different picture, with Obama shown to be leading a poll of 957 likely voters, 51 percent to 47 percent.

"Obama's up 56/43 with women and 92/8 with African Americans and he's holding Romney to a 58/40 advantage with whites, which is below what we've generally been finding for him nationally recently," the poll explains.

The Democrats are also in leading position to win US Senate races in Virginia, Public Policy Polling finds, with Tim Kaine leading George Allen 52/46 in Virginia's open seat race.

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