President Obama scored a modest win in the third presidential debate, according to the latest Washington Post-ABC News tracking poll, but it’s Republican Mitt Romney who moved the needle among likely voters -- including independents -- with his debate performances.

Overall, the contest remains unchanged from Tuesday, with 49 percent of likely voters nationally backing Romney, and 48 percent supporting Obama. But as was the case after the first and second debates, more voters say they have better, not worse, opinions of the former Massachusetts governor when assessing the three debates.

Most say the president’s debate performances did not change their views of him, a continuing challenge for an incumbent stuck with an approval rating in dangerous territory: 50 percent of likely voters approve of how he’s handling the job, 49 percent disapprove.

Obama is also at just 50 percent among likely voters, with Romney at a close 45 percent, as the one who better understands the economic problems people are having today. That five-point gap is an apparent -- but not significant -- edge for the president, and is as small as it has been all year. Romney has a six-percentage-point lead on handling the economy itself.

Among political independents, 49 percent say Romney is the one who is more empathetic with ongoing economic woes; 45 percent say Obama is more in tune. That’s not a statistically significant advantage for the challenger, but does represent a directional shift from before the first debate.

Looking at handling the economy as a broad issue, Romney’s lead among independents has swelled to 56 to 39 percent in the new poll, an advantage that helps him to a sizable, 12-point lead over Obama when it comes to their voting preferences. Obama won independent and other voters by eight percentage points in 2008.

Across all three debates, 40 percent of independents say their impressions of Romney improved; fewer than half as many, 18 percent, say their views deteriorated. Twice as many independents say their views of Obama are worse as say better, 20 percent to 10 percent.

The Post-ABC tracking poll is a series of consecutive one-night “waves” of interviews reported as a rolling, multi-night average. The new results are for interviews conducted Oct. 20-23, among a random sample of 1,394 likely voters. At this point, only one of the four waves includes interviews conducted entirely after Monday’s debate.

Results for this sample have a margin of sampling error of plus or minus three percentage points. Question wording, results and methodology available here.