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TALLAHASSEE (CBSMiami/NSF) – Florida’s high-stakes U.S. Senate race is tightening, with incumbent Republican Marco Rubio holding a three-point edge over Democratic challenger Patrick Murphy, according to a poll released Thursday.

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Peter A. Brown, assistant director of the Quinnipiac University Poll, said the closeness of the race could be linked to recent struggles of controversial Republican presidential nominee Donald Trump — with the presidential race having an effect “down the ballot.”

“At this stage of the campaign, Republican U.S. Senate candidates may be running against their own presidential nominee, Donald Trump, as much as they are against their Democratic opponents,” Brown said in comments released Thursday morning with the poll results.

Murphy, who faces fellow Democratic Congressman Alan Grayson in an Aug. 30 primary, trailed Rubio by a margin of 50 percent to 37 percent in a Quinnipiac poll released July 14. But Thursday’s results showed Rubio ahead 48-45 percent.

Similarly, Grayson trailed Rubio by 12 points in the July poll but was down by a margin of 49 percent to 43 percent in Thursday’s poll.

Rubio, who is seeking a second term in the Senate after a failed bid for the Republican presidential nomination, faces an Aug. 30 primary against businessman Carlos Beruff. The Quinipiac poll showed Murphy with a 14-point lead over Beruff in a head-to-head matchup, while Grayson led Beruff by four points.

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The poll of 1,056 likely Florida voters was conducted from July 30 to Sunday and had a margin of error of 3 percentage points — matching Rubio’s lead over Murphy.

Races this year for Republican-held seats in states such as Florida, Ohio, Pennsylvania, Illinois, Wisconsin and New Hampshire could largely determine whether the GOP retains control of the Senate. During his presidential campaign, Rubio repeatedly said he would not seek re-election — but changed his mind in June after urging from GOP officials including Senate Majority Leader Mitch McConnell, R-Ky.

Murphy, meanwhile, has backing from many state and national Democratic leaders, including President Barack Obama. As an indication of that support, Vice President Joe Biden appeared last week at a Tallahassee fundraiser for Murphy.

The poll released Thursday by the Connecticut-based Quinnipiac showed Rubio comfortably leading Murphy and Grayson among independent voters. Otherwise, the numbers were similar to trends in the presidential race in Florida, with Rubio doing well among male and white voters and the Democratic candidates holding hefty leads among non-white voters.

“Sen. Rubio’s 10-point lead among independent voters over Congressman Patrick Murphy and his eight-point edge over Congressman Alan Grayson is the Republican’s best weapon in his reelection race,” Brown said.

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The News Service of Florida’s Jim Saunders contributed to this report.