A new poll shows President Obama holding a narrow lead over Republican Mitt Romney in Florida — with the state still living up to its toss-up status.

While Obama appeared to be widening his distance over Romney nationwide last week, Suffolk’s survey of 600 registered voters in Florida shows Obama’s 3 percentage point lead remains within the poll’s margin-of-error. Obama was up 46-43 percent, with seven percent of voters undecided.

“On the eve of the first debate, both Barack Obama and Mitt Romney know the importance of each percentage point in a state like Florida,” said David Paleologos, director of the Suffolk University Political Research Center in Boston.  “Not only are the remaining undecided voters critical, but so are the voters of all the third-party candidates here – and there are many.”

 The Suffolk University/7NEWS (WSVN-Miami) survey is the first taken in Florida this year that includes all 12 of the candidates who qualified to appear as presidential contenders on the Florida ballot.

 Libertarian Gary Johnson, Green Party nominee Jill Stein, and Peace and Freedom Party nominee Roseanne Barr were each favored by 1 percent of voters polled. In a state where the George W. Bush and Al Gore’s epic 2000 election deadlock was helped by third-party candidate Ralph Nader, these also-rans could loom as a factor in Florida’s final count.

The Florida Senate race also looks tougher to call in Suffolk’s survey.

Although Democrat Bill Nelson has built a commanding lead in many polls, Suffolk showed him holding a 40-34 percent lead over Republican Connie Mack, with 20 percent of voters still undecided.

 Other contenders on the Florida Senate ballot, Chris Borgia and Bill Gaylor, gain 4 percent and 1 percent, respectively, of the vote in the poll.

Gov. Rick Scott gets something like good news on his approval ratings in a new survey by Suffolk University and WSVN-TV-Miami.

The poll shows 42 percent of voters like the job he’s doing as governor — compared with 44 percent who disapprove. The disapproval rating is better than the chilling 54 percent marks Scott earned in late April in two separate surveys, Public Policy Polling and Rasmussen Reports.

While PPP found Scott’s approval still hovered low — at 34 percent, Rasmussen gave Scott better numbers — 43 percent backing from voters.

The Post reported earlier this week that the Republican Party of Florida has paid almost $1 million since March for a TV campaign, promoting the governor’s push for $1 billion more for public schools and helping state unemployment fall to a three-year low behind what the ads label Scott’s “pro-business initiatives.”

But with his barnacle-scraping approval ratings, Scott is likely to emerge this election season as a candidate Democrats and their allies seek to tie to presumptive Republican presidential nominee Mitt Romney.

“Rick Scott’s not on the ballot, but the philosophy he espouses will be, and that’s what will be our focus,” said Rich Templin, a spokesman for the Florida AFL-CIO, which represents 500,000 workers in the state.