Obama took 48 percent support in the poll to Romney's 46. Florida is still a toss-up, according to the Real Clear Politics average of polls, with each candidate taking 47 percent support.

Romney accepted the GOP’s presidential nomination at the Republican National Convention in Tampa, Fla., late last month, but he failed to receive much of a bounce coming out of it.

The Rasmussen poll of 500 likely voters was conducted Sept. 12 and has a 4.5 percentage point margin of error.