President Obama is clinging to a slender four-point lead over Republican Mitt Romney in Virginia as both sides ramp up already aggressive campaigns in the crucial battleground state, according to a new Washington Post poll.

Obama outpolled Romney, 51 to 47 percent, among likely Virginia voters, although he lost the clearer 52-to-44 percent advantage he held in mid-September.

Unlike in the Washington Post-ABC News national tracking poll, Obama still has an edge when Virginia voters are asked who better understands people’s financial problems, and he has not fallen behind a surging Romney on the question of who would better handle the national economy. Nor has Obama lost significant ground among self-identified independents in Virginia, as he has nationally.

The results underscore the importance of swing states like Virginia, with its 13 electoral votes, as both campaigns seek to secure a path to the 270 electoral votes needed for victory.

Perhaps the poll’s most striking insight concerns the many voters the two campaigns have contacted in Virginia this fall. A staggering 44 percent of likely voters polled said they had been contacted by the Obama campaign; 41 percent said the same of Romney’s. More than one in four had heard from both campaigns.

The race to win the battleground state of Virginia

Both campaigns have increased efforts to reach voters since last month, although fewer voters said they had been contacted by Obama’s team this time than four years ago. Romney’s organization, meanwhile, is outperforming Sen. John McCain’s in 2008.

In addition, as if to confirm both sides’ emphasis on early voting, 4 percent of likely voters polled said they had already voted by absentee ballot. An additional 41 percent said they were likely to do so, which would be a sharp jump from four years ago.

The numbers reflect the intensity of the two campaigns in Virginia. Obama has attended 19 political events in the state this year, including a rally in Richmond last week and another scheduled for Monday in Prince William County. Romney has attended 20 political events in the state since winning the Republican nomination, and he would have attended a 21st on Sunday had it not been canceled in advance of Hurricane Sandy.

Virginia, like Ohio and Florida, is particularly critical for Romney, whose path to the White House would be difficult without the state’s electoral votes.

Both candidates see a route to victory in Virginia. Obama is counting heavily on his advantages among African American, Latino and female voters as well as on his support in Washington’s inner suburbs and the urban centers of Richmond and Hampton Roads.

Romney, meanwhile, hopes to gin up big turnouts in such Republican-leaning places as Chesterfield, near Richmond, and Virginia Beach, as well as in conservative, coal-friendly strongholds in southwest Virginia. The new polling numbers suggest that Romney might be succeeding. In the new poll, he leads overwhelmingly (60 percent to 39 percent) in the central and western regions of the state, much improved from a seven-point advantage in mid-September.

“From an economic standpoint, I think the national debt is the key issue,” said Donald Lewis of Salem, in southwest Virginia. Lewis, a retired middle manager for Norfolk Southern Railway, said he will vote for Romney because he thinks the Republican would do a better job of straightening out the nation’s finances. “We have to concentrate on getting our budget balanced and our debt under control before it turns into riots like in Europe,” Lewis said.

The nation’s fiscal health — and the federal deficit — is one of the few subjects on which Romney has an advantage over Obama in Virginia. But in Virginia, unlike in national polls, Romney does not have a clear lead on the economy, and he continues to trail on other issues. Romney trails by 10 points on the question of who would better manage the future of Medicare; by 13 points on who better understands Americans’ economic problems; and by 12 points on who is better equipped to manage international affairs.

Obama also enjoys a wide lead among likely voters (56 percent to 35 percent) on the question of social issues, such as abortion and same-sex marriage.

Statewide, Romney and Obama are running nearly even on whom voters trust more to handle military spending, with the Republican neutralizing an advantage since September. Romney has taken a 13-point lead on the issue in Washington’s outer suburbs, including Loudoun, Fauquier and Prince William counties. In the inner suburbs, Obama continues to hold a wide lead.

Romney is also winning among military veterans and service members on active duty. His lead, 59 percent to 38 percent, is a dramatic improvement from September, when the split was 51 percent to 47 percent.

Both campaigns are at least as focused on motivating partisans as persuading swing voters. Just over half of likely self-identified independent voters in the inner Washington suburbs, for instance, have been contacted by either campaign, compared with more than six in 10 of those who identify with a particular party.

In Virginia, contrary to the most recent national numbers, Obama has an edge on enthusiasm: Among his backers, 70 percent are “very enthusiastic” about his candidacy, compared with 56 percent of those who back Romney. But Obama’s supporters appear to need more of a nudge than Romney’s do. Ninety percent of Democrats contacted by Obama said they are “absolutely certain” they’ll vote, compared with 82 percent who had not been contacted; among Republicans, more than nine in 10 said they are certain to vote regardless of whether they had been contacted.

More broadly, the poll shows that the 2012 electorate in Virginia is shaping up as similar, though slightly less Democratic, than the state’s electorate in 2008.

The poll was conducted among a random sample of 1,504 adults from Oct. 22 through Oct. 26 on conventional and cellular phones. Among the sample of 1,228 likely voters, the poll carries a margin of error of plus or minus 3.5 percentage points.

Jon Cohen, Peyton M. Craighill, Errin Haines, Rachel S. Karas, Ben Pershing and Laura Vozzella contributed to this report.