Former Congressmen Patrick Murphy and David Jolly are exploring a bipartisan run for governor, a surprise move that hinges on polling Democrat Murphy has commissioned this week.

Murphy would run for the Democratic nomination as Jolly, a moderate Republican and prominent anti-Trump voice on cable news, would have no chance of winning a GOP primary.

UPDATE: In a text message, Murphy said, "Some supporters wanted to do a poll and I didn't say no. I certainly didn't say yes to actually running!"

The men have become friends over the past year as they've gone across the country on a town-hall style tour about gridlock and dysfunction in Washington.

Murphy, 35, lost a Senate race to Marco Rubio in 2016. Jolly, 45, lost his re-election bid the same year against Charlie Crist.

The split ticket idea recognizes growing dissatisfaction with the polarization of both parties and a possible "third way."

But the challenges remain immense and Murphy and Jolly would have to overcome fundraising and other challenges in a state Donald Trump narrowly won – though Trump himself blurred party lines at times and ran against the political system.

"Working across the aisle was a hallmark of my two terms in Congress, and the relationships I formed with members of both parties were invaluable," Murphy said at the outset of the town-hall tour last summer. "I look forward to joining my former colleague as we share our perspectives on ways we must work together to improve our broken political system."

Jolly added, "Even in times of great disagreement there are ways of finding common ground, there are opportunities for bipartisan leadership to solve some of our country's toughest issues."