MIAMI—Marco Rubio and John Kasich face judgment day Tuesday, fighting for their political lives in their home states of Florida and Ohio, where they've been elected with overwhelming margins in the past. Their struggle to win back their constituents is emblematic of the course of a Republican primary dominated by front-runner Donald Trump.

Florida and Ohio are the crown jewels of the Republican race for the White House, as the victor in each state wins all of its delegates. A sweep by Trump in these states, which are also key general election battlegrounds, would put him on a clearer path to the nomination. Both Rubio and Kasich return to home court as underdogs aiming to prevent that scenario.

Heading into Election Day, however, it appears unlikely that both hometown sons will succeed simultaneously. According to polling, Gov. Kasich has a better shot of defeating Trump in Ohio than Sen. Rubio does in Florida. The RealClearPolitics average finds the billionaire businessman-turned-GOP-front-runner virtually tied with Kasich while leading Rubio by nearly 20 points.

The notion that Kasich might outlast Rubio in the race seemed unimaginable just months ago. But this campaign has produced all sorts of surprises and turns. One of them came in New Hampshire last month, when Rubio faltered after a poor debate performance and Kasich surged to the coveted second-place spot.

With their like-minded rivals now out of the race, Kasich and Rubio emerged as the last hopes of a Trump alternative for what remains of the Republican establishment. Both candidates barnstormed their respective states over the past few days hoping to change the trajectory of the race. But there was also a difference in style that signaled the days ahead.

Rubio railed against what he sees as Trump’s creation of a toxic environment that threatens to tear the party apart. “I don’t think there’s anyone in the history of American politics that compares to the vulgarity of a Donald Trump candidacy,” he told reporters at a stop in Melbourne, Fla., his second of four events on Monday, including one in Palm Beach that drew nearly 2,000 supporters. The primary would be a choice between "optimism and fear," he said at one stop. "We're not going to allow the conservative movement to be hijacked," he said at another.

Rubio closed out his Florida campaign with an election eve rally at a park near his west Miami home. It was a warm but breezy evening, and the affair felt much like a large neighborhood gathering. As he stood in the bed of a pickup truck parked on the basketball court, Rubio addressed the crowd in English and Spanish. Speaking through a bullhorn that was at times hard to hear, he urged his neighbors to vote. As he has so many times throughout this election, he told them the campaign had shown that a product of this neighborhood could ascend to the White House. "No matter where I go or what I'll be, I'll always be a son of this community," he said. Many in the audience were confident he could fulfill such a prophecy at some point, if not this time. "Never give up, Marco!" shouted a man in the crowd.

If Rubio wins Florida, it will be considered one of the greatest upsets of the cycle, which speaks to the hold Trump has had on most elements of the campaign. Not too long ago, Rubio's greatest challenge in his home state was overcoming Jeb Bush, the former Florida governor who had deep loyalties in the state. The fact that Rubio outlasted his former mentor is noteworthy, but the same force that made Bush an also-ran now threatens Rubio.

Trump has so far proven to be the agent of change in American politics that Rubio had hoped to embody, though in a very different way. A debate stage fumble and a late-in-the-game shift in strategy, which Rubio has publically regretted, also contributed to his rocky road.

Meanwhile, Kasich has surged in his home state, appearing at more than 10 events in the days leading up to the primary and asking voters to reward the positive, uplifting campaign he’s run.

A sign that Kasich might have eclipsed Rubio came Monday, when on the eve of the all-important primary, the party's former standard-bearer, Mitt Romney, went to Ohio to campaign for the governor. The visit was part of Romney's anti-Trump push and not billed as an endorsement. But with just hours to go until voters would weigh in, the writing seemed to be on the wall.

"You look at this guy and unlike the other people running, he has a real track record," Romney said at an airport hangar in North Canton, Ohio. "He has the kind of record that you want in Washington. That’s why I’m convinced you’re going to do the right thing tomorrow — agreed?"

For his part, Kasich dismissed the idea of inheriting the establishment mantle.

"I've never been the establishment's first, last or whatever hope. I'm not part of the establishment," he told reporters Monday. "I've always made them nervous and I will continue to make them nervous because I'm a change agent."

Both Kasich and Rubio are aiming to prevent Trump from winning the requisite number of delegates to secure the GOP nomination outright — a strategy that would likely lead to a contested national convention.

"I am not running to block anybody from anything," Kasich insisted. "But the math is real. And if somebody can't get the number of delegates – look, we've got 1,000 delegates left to go. And you will see me pick up speed and have momentum. I may go to the convention and have more delegates than anyone. But probably not enough to win."

Trump, for his part, has held multiple rallies in both Ohio and Florida in the last week, hoping wins in both states would put his campaign on an unstoppable path to the nomination. In an indication of where Trump sees Tuesday’s races, he cancelled an event in Florida Monday and added a stop in Ohio on the eve of the primary.

Kasich has enviable approval ratings among Republicans in his home state, and energized voters at each of his rallies seem excited to support him.

John Mueller, 49, an e-commerce worker in Canton, said he sees real momentum for Kasich.

“I think he may come from behind,” Mueller said. “Just because he didn’t get to the top right off the bat, I don’t think it’s a bad thing. I think he’s just slowly gaining the momentum he needs.”

Sally Kindsvatter, an 81-year-old retired hospital lab microbiologist, said she sees Kasich as Republicans’ last chance to stop Trump.

“I think he’s our only hope for president that will bring our country together and maybe serve as a real leader,” Kindsvatter said. “He’s the only hope we have. I consider myself a moderate Republican, and no Republicans represent me anymore. I’m either voting for Kasich or Hillary Clinton.”

If Kasich is successful in Ohio, it will still be his only primary victory, with half the states having already voted. And the map ahead could continue to be challenging. The governor insists he will do well in similar states such as Pennsylvania and New York, but Trump's decisive win in Michigan last week and his positioning in Illinois, which also votes on Tuesday, underscores how difficult this race is for other candidates, even on their home turf.

What's more, Ted Cruz, who won his home state of Texas (though not all its delegates), is keeping pace with Trump more so than the other rivals. The senator figures to peel off many more delegates on Tuesday night in Illinois, Missouri, and North Carolina, keeping somewhat under the radar while the attention is paid to Kasich and Rubio.

All in all, Tuesday represents a binary for both Kasich and Rubio: either a come-from-behind resurgence and momentum going into the second half of the primary, or the end of their presidential campaigns.

James Arkin reported from Ohio.

James Arkin is a congressional reporter for RealClearPolitics. He can be reached at jarkin@realclearpolitics.com. Follow him on Twitter @JamesArkin.