President Barack Obama held on to a slim lead over Mitt Romney in three national polls Monday, as he appeared to have stemmed the bleeding after his poor first debate.

Three weeks and a day before the election, Obama leads Romney by two percentage points in the Reuters/Ipsos daily tracking poll, with 47 percent support from likely voters in the national online poll, compared with 45 percent support for Romney.

In an ABC News/Washington Post survey, Obama was up 49 to 46 percent. The Politico/George Washington University Battleground Poll had the president leading by 49 to 48 percent, but Romney led by an average of two points in 10 swing states.

In Gallup’s daily tracking poll released Monday, however, Romney led 49 to 47 percent among likely voters, while Obama was ahead 48 to 46 among registered voters. A USA Today-Gallup poll gave Romney a five-point lead across 12 swing states.

"In every poll, we've seen a major surge among women in favorability for Romney," Democratic pollster Celinda Lake told USA Today about the race after the first presidential debate. "Women went into the debate actively disliking Romney, and they came out thinking he might understand their lives and might be able to get something done for them."

The Reuters-Ipsos margin was small enough to be a virtual tie, but Obama's slight edge broadened from Sunday, when he went ahead of Romney by 1 point after falling behind in the wake of Romney's decisive victory in their first debate on Oct. 3.

"Romney received a bump from that first debate, but the very nature of a bump is it recedes again," Ipsos vice president Julia Clark said. "We're now seeing Obama regaining a little bit of a foothold as we go into the second debate. They go into the debate on equal footing."

The two men meet again on Tuesday night at New York's Hofstra University in a debate that Obama desperately needs to win. The third debate is next Monday in Boca Raton, Fla.

Obama's support in the new Reuters/Ipsos survey was particularly strong -- 55 to 43 percent -- among the 10 percent of registered voters who have already cast their ballots.

Romney and the Republicans have been hitting Obama hard over his handling of diplomatic security, blaming his administration for attacks in Egypt and Libya on Sept. 11. The U.S. ambassador and three other Americans were killed in Libya.

But the poll did not find a groundswell of condemnation for the White House. Forty-five percent of registered voters approved of Obama's handling of the situation in Libya and Egypt and 40 percent disapproved. Thirty-eight percent backed Romney on the issue, compared with 36 percent who did not.

The incumbent also regained ground on several issues since the first week after his poor first debate performance.

Forty-two percent of registered voters said they thought Obama had a better plan for health care, compared with 35 percent for Romney. Obama's rating was up 4 points from last week.

Obama's ratings on taxes also went up by four points, as did voters' view of his plans for Social Security and Medicare, by 3 points each.

Romney's scores each went up by 3 points on how he would handle the war on terrorism, and gay marriage, although Obama was still ahead on both.

Thirty-seven percent of registered voters picked Obama as having better policies for dealing with terrorism, compared with 32 percent for Romney. And 43 percent favored Obama on gay marriage, which he has endorsed, compared with Romney's 25 percent.

Romney kept a big lead of 38 percent to 29 percent on the question of who has a better plan for handling the deficit, and he held a small lead of 38-37 percent on the question of who would better handle the U.S. economy. Obama was just ahead, at 39 percent to 38 percent, on jobs and employment.