Susan Page

USA TODAY

Hillary Clinton now leads Donald Trump in the key state of Florida, a newSuffolk University Poll finds, another sign of a bounce in support for the Democratic presidential nominee in the wake of the national political conventions and controversies that have enveloped her Republican rival.

In the survey, Clinton leads Trump 48%-42% in a two-way race. That's an improvement for her from other recent Sunshine State polls averaged by RealClearPolitics, which had shown the two tied at 44%-44%.

Other polls released Wednesday in Michigan, New Hampshire and Pennsylvania — swing states all — also show Clinton gaining ground, scoring leads ranging from nine to 15 percentage points.

In Florida, Clinton's edge narrows to four points when Libertarian nominee Gary Johnson and Jill Stein of the Green Party are added to the ballot. In a four-way contest, Clinton is at 43% and Trump at 39%, with Johnson at 4% and Stein at 3%. When more options are mentioned, the number of undecided voters rises a tick, to 11% from 9% in the two-way race.

"It's a given that Trump continues to lose among women and south Florida voters, but his biggest challenge is keeping registered Republicans from defecting and winning over independents," says David Paleologos. director of Suffolk's Political Research Center. Trump trounces Clinton among Republicans, but she trounces him by even more among Democrats. Among independents, Clinton leads by a narrow 42%-40%.

Eighteen percent of independents remain undecided, double the proportion among likely voters overall.

Another poll shows Clinton opening up lead over Trump

Polls: Clinton pulls ahead of Trump after convention

The survey of 500 likely Florida voters, taken Monday through Wednesday, has a margin of error of plus or minus 4.4 points.

Distaste for Clinton is motivating many Trump voters. While 52% of his supporters say their vote is mostly for him, 39% say it is mostly against her. When it comes to Clinton voters, though, 67% are voting mostly for her; 28% mostly against him.

Trump's troubles haven't sunk the fortunes of Florida Sen. Marco Rubio, seeking a second term after abandoning his bid for the GOP's presidential nomination. Rubio leads both of the most likely Democratic candidates, Rep. Patrick Murphy (by 13 points, 46%-33%) and Rep. Alan Grayson (by 14 points, 45%-31%).

For the Aug. 30 primary, Rubio easily dispatches his Republican challengers, with 62% of the vote against the field. Miami real-estate developer Carlos Beruff is at 12%.

In the Democratic primary, Murphy leads Grayson by 2-1, 36%-17%. That said, 40% of likely Democratic voters say they are undecided.

Trump campaigned Wednesday at two massive rallies in Florida, which looms as a critical swing state in November.

On a list of 13 issues facing the next president, only three topics were rated “most important” by 10% or more of poll respondents: terrorism/national security, cited by 26%; jobs/economy, by 18%, and choosing Supreme Court nominees, by 10%. Issues such as climate change, health, education and guns trail in distant single digits. Even illegal immigration, the issue that has energized Trump's campaign from the start and is a major concern in Florida, is named by just 5% as the “most important” issue.

In response to a separate question, three of four Floridians express concern about the Zika virus spreading in the United States. More than four in 10 say they are "very" concerned.