The two Republican Senate incumbents in Florida and Pennsylvania are locked in tight re-election battles, while Ohio's GOP senator has opened up a near double-digit lead, according to a new poll.

According to a new Quinnipiac University poll released Thursday, Republican Sen. Marco Rubio is ahead of Democratic Rep. Patrick Murphy in Florida by just 3 points — 48 percent to 45 percent. Rubio leads other Democratic hopeful Rep. Alan Grayson by a bit more, 49 percent to 43 percent.

In Pennsylvania, Democratic challenger Katie McGinty has pulled ahead of GOP incumbent Pat Toomey by a slim 3-point margin of 47 percent to 44 percent.

Ohio Sen. Rob Portman is in decent standing against former Gov. Ted Strickland in that Senate race, though the latter is still within striking distance. Portman leads Strickland by 9 points, 49 percent to 40 percent.

The three swing states' Senate races are just as important as how they vote in the general election. Since 1960, no candidate has won the presidential race without taking at least two of the three states. Quinnipiac University's presidential race poll released this week shows Democratic nominee Hillary Clinton and Republican nominee Donald Trump are tied in Florida, while Clinton has a small lead in Ohio and surging in Pennsylvania.

Republicans are also looking to hold a majority in the Senate this fall.

"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," said Peter A. Brown, assistant director of the Quinnipiac University Poll.

Brown explained that the incumbent senators seeking re-election are "running better than Trump. But if Trump continues to lag behind in the presidential race, that will make it more difficult for GOP candidates, logic holds, up and down the ballot."

The telephone-based survey was conducted July 30-Aug. 7. It surveyed 1,056 Florida voters, carrying a margin of error of plus or minus 3 percentage points. The margin of error for both Ohio (812 voters) and Pennsylvania (815 voters) is plus or minus 3.4 percentage points.