 -- President Barack Obama leads Mitt Romney in Florida, Ohio and Virginia, according to new polls of the key 2012 swing states, although Obama's advantage has narrowed in recent months.

Obama has inched ahead of Romney 48 percent to 44 percent in both Florida and Virginia, according to three new NBC News/Marist polls. In Ohio, the president has a 6-point advantage over Romney, leading his Republican rival 48 percent to 42 percent among registered voters in the state. (The polls have a plus or minus 3 percent margin of error.)

Despite the good news, there are signs of danger for the Obama campaign. In March, the same polls found Obama with a 12-point lead over Romney in Ohio and a 17-point lead in Virginia. In January, the poll had Obama besting Romney by 8 points in Florida.

A few key findings benefit Obama. A majority of voters in all three states believe the "worst is behind us" when it comes to the economy, according to the polls—though less than 40 percent of voters think the economy will get better over the next year. Meanwhile, 57 percent of voters in Ohio and Virginia and 56 percent in Florida think Obama "inherited" the struggling economy—a finding that could test Romney's argument that Obama's policies made things worse for the country.

Yet Obama and Romney are statistically tied in all three states when it comes to the question of which candidate would best handle the economy. A plurality of voters in these states believe Romney is the best candidate to handle the national debt.

While Romney's numbers are on the rebound, the polls found one key hurdle for the presumptive Republican nominee: His favorability numbers continue to lag behind Obama's.

In Ohio and Virginia, Obama holds a 10-point advantage or more over Romney when it comes to the percentage of voters who hold a "favorable" impression of the candidate. In Florida, the margin is narrower, but voters are still statistically split on how they view Romney: 45 percent hold a favorable view, compared to 43 percent who hold an unfavorable one.

More popular Yahoo! News stories:

• Romney: 'Of course' Bain should be an issue, but campaign is about Obama's record

• Obama touts support for gay marriage in Jane Lynch-narrated video

• Romney's education plan: Low-income students can attend any public school they want

Want more of our best political stories? Visit The Ticket or connect with us on Facebook, follow us on Twitter, or add us on Tumblr. Handy with a camera? Join our Election 2012 Flickr group to submit your photos of the campaign in action.