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MIAMI (CBSMiami) – A late entry into the race, incumbent Senator Marco Rubio has a sizeable lead over his opponents, according to a new Quinnipiac University Swing State Poll.

In Florida, Rubio led U.S. Rep. Patrick Murphy by a margin of 50 percent to 37 percent. Rubio led U.S. Rep. Alan Grayson, another possible Democratic challenger, by a margin of 50 percent to 38 percent.

Rubio led Murphy 54 percent to 33 percent among men and 47 percent to 40 percent among women, with similar results in a Rubio-Grayson matchup.

“Democrats made fun of Sen. Marco Rubio when he opted for a last-minute re-election bid in Florida, but he may be on the way to a last laugh, having quickly opened double digit leads over both Democratic challengers,” said Peter A. Brown, assistant director of the Quinnipiac University Poll.

In Ohio, former Goveror Ted Strickland, who had an early lead now trails Senator Rob Portman by 7 percentage points (47 percent to 40 percent).

In Pennsylvania, Sen. Pat Toomey held a 10 point lead over Democrat Katie McGinty (49 percent to 39 percent).

“The numbers seem to be breaking the Republican way in the battle for control of the U.S. Senate, at least when it comes to the critical swing states of Florida, Ohio and Pennsylvania,” said Brown. “Many talking heads have suggested that with Donald Trump at the top of the GOP ticket, Republican Senate candidates might suffer. But at least in these three key states, the Republican Senate candidates are running ahead of Trump and don’t seem to be hurt by their shared party label.”

The Swing State Poll focused on Florida, Ohio and Pennsylvania because since 1960 no candidate has won the presidential race without taking at least two of these three states.