Mitt Romney has built a slight lead on President Obama in Florida, according to a new poll from independent pollster Mason-Dixon.

The poll shows Romney at 51 percent and Obama at 44 percent. In mid-September, the same pollster had Obama at 48 percent and Romney at 47 percent.

The poll comes on the heels of a series of swing state polls from earlier Thursday that showed very little change in the swing states, despite indications that Romney has gained momentum nationally.

Notably, a poll from NBC News and Marist College released earlier Thursday showed the race virtually unchanged in Florida, with Obama at 48 percent and Romney at 47 percent.

It remains to be seen if this is a momentary bump for Romney in Florida and whether other polling will back it up. But for a campaign that remains in search of significant swing-state momentum, it's a good sign.

The poll shows the debate last week had a direct impact on voters, with 5 percent saying they were undecided but now support Romney, 2 percent moving from Obama to Romney and 2 percent moving from Obama to undecided. There was no movement in the other direction (away from Romney).

The survey also shows Romney's personal image, for once, is better than Obama's. Fifty percent of voters view Romney favorably, compared to 45 percent who view Obama favorably.

Romney also leads in every portion of the state except the southeast, and he's about even with Obama among Hispanics, who went 57 percent for the president in 2008. The poll has 46 percent of Hispanics going for Romney and 44 percent going for Obama.