A new poll shows President Obama and GOP challenger Mitt Romney locked in a virtual tie ahead of their second debate.

The latest Washington Post/ABC News poll shows Obama with a 49 to 46 percent lead among likely voters, an edge little changed from the same poll taken in late September, which gave the president a 49-47 percent lead over Romney.

Most respondents say there is little chance they will swing their vote in the three weeks left until Election Day, with 90 percent saying they will definitely vote for the candidate they back now and 9 percent saying there remains a chance they could change their minds. But only 2 percent peg the odds of them switching their vote as “good,” with 7 percent saying that remains “unlikely.”

Voters surveyed in nine battleground states — Colorado, Florida, Iowa, Nevada, New Hampshire, North Carolina, Ohio, Virginia and Wisconsin — break for Obama, 51 to 46 percent.

The Washington Post/ABC poll is only the latest in a number of surveys that show the presidential race tightening after the Oct. 3 debate in Denver, which Romney was widely considered to have won. Gallup’s daily tracking survey of likely voters has Romney up 2 points with a 49-47 percent edge, and multiple polls show him in a statistical dead heat with Obama in key swing states.

Overall, voters continue to favor the job Obama is doing, with 50 percent approving and 48 percent disapproving.

But there are still worrisome signs on the economy and the country’s track for the Obama campaign. Fifty-six percent of registered voters say the country is headed on the wrong track, with 42 saying the country is headed in the right direction. That figure, though, is better news for Obama than results from the same poll in August, which showed a 29 percent right track to 69 percent wrong track split.

Romney received a strong boost from the first presidential debate. Before that debate, 59 percent of Obama supporters and 52 percent of Romney backers said they were “very enthusiastic” about backing their candidates. Now, 60 percent of Obama backers are very enthusiastic, as are 62 percent of Romney supporters.

Thirty-five percent said their opinion of Romney changed for the better after the first debate, with 14 percent saying it grew worse and 48 percent seeing no change. Seventy percent said the debate didn’t change their mind on Obama, with 9 percent viewing him better post-debate and 19 percent worse. 

Romney, though, continues to trail Obama on ratings of honesty and personal likeability. 

Voters rate Obama as more honest and trustworthy, with 55 percent saying he has those qualities to 41 percent who disagree. Voters are evenly split on Romney at 47-47 percent. Fifty-eight percent say Obama seems more friendly and likeable than Romney, at 32 percent. 

Fifty-one percent say Obama better understands the economic problems facing voters, to 42 percent for Romney.

The poll also finds Obama holding the edge over Romney on a number of key issues. Voters say they trust Obama to handle the economy over Romney by 48 to 47 percent. Obama also holds the edge on taxes 48-46 percent, and on healthcare, 47-46 percent. Romney holds a strong advantage, though, on tackling the deficit, with voters saying they trust the GOP nominee 51 to 43 percent. 

On international affairs, Obama holds a 50-43 percent edge. Republicans have made the deaths of four Americans in an attack on the U.S. Consulate in Benghazi, Libya, last month a centerpiece of their attempts to paint the Obama administration as weak on foreign policy. But the polling suggests those criticisms may not be resonating with voters.

Obama leads by 9 points when voters were asked who they would trust to handle an unexpected major crisis, 52-43 percent.

The poll was conducted from Oct. 10 to 13 and has a 3.5-point margin of error.