New polls show Sen. Marco Rubio trailing Donald Trump badly in his home state of Florida – even dropping to third place behind Ted Cruz in one – while Ohio Gov. John Kasich, too, is locked in a dogfight with the Republican primary front-runner in his home state ahead of crucial primaries Tuesday.

The latest Marist/NBC/Wall Street Journal poll shows Trump dominating Rubio with a double-digit lead in Florida, 43-22 percent. The same poll shows Cruz essentially tied with Rubio, at 21 percent. A separate CBS News 2016 Battleground Tracker poll shows Rubio slipping behind Cruz.

Meanwhile, in Ohio, a Marist survey shows Kasich holding the edge in the Buckeye State with 39 percent to Trump’s 33 percent. The latest Quinnipiac poll shows Trump and Kasich tied in Ohio, with 38 percent each.

The primaries in Ohio and Florida, among five Tuesday, are essentially a must-win for both Kasich and Rubio, respectively – both of whom significantly trail front-runner Trump and Texas Sen. Cruz in the delegate count.

Rubio’s drop in the polls appears to be another indication that his campaign might soon come to an end.

On Sunday, he continued to criticize the violence at Trump rallies, saying the candidate and protesters share the blame.

"You have a leading contender for president telling people in his audience, ‘Go ahead and punch someone in the face. I'll pay your legal bills,’ ” Rubio said in Florida. “That's wrong if our kids did it. That is disastrous if a president does it.” He has also acknowledged that some of the protesters appeared to be paid.

The CBS News 2016 Battleground Tracker poll showed Rubio falling even further.

It showed Trump -- who has several, popular golf-resort properties in Florida -- maintaining his lead in the state’s winner-take-all primary, in which 99 delegates are at stake.

The billionaire businessman has 44 percent of the vote among registered voters in the state, compared with Cruz at 24 percent and Rubio at 21 percent.

At a rally Sunday in Ohio, Trump tried to portray Rubio as an unpopular senator who was elected in 2010 to go to Congress but has since repeatedly missed votes to instead campaign and further his political career.

The poll, conducted by the YouGov an online polling group, shows Trump and Ohio Gov. John Kasich, the remaining GOP presidential candidate, in a dead heat in Ohio, at 33 percent. They are followed by Cruz at 27 percent and Rubio at 5 percent.

On Sunday, Trump hit Kasich at rallies, including one in the Cincinnati area, for voting as a congressman in favor of the roughly 20-year-old North American Free Trade Agreement that critics say has taken away millions of manufacturing jobs, especially ones in so-called Rust Belt states such as Michigan, Illinois and Ohio.

Kasich faces a similar situation as Rubio, needing to win in his home state to keep his campaign headed toward the GOP convention in July.

The popular governor has repeatedly vowed that he will win Ohio and that he will drop out if he loses the primary, in which the winner gets all 66 delegates.

Trump leads the delegate count 460, followed by Cruz with 370, Rubio with 163 and Kasich, who has yet to win a primary or caucus, with 63.

The three other states on Tuesday also holding primaries are North Carolina (72 delegates), Missouri (52 delegates) and Illinois (69 delegates.)

Trump also leads in Illinois -- 38 percent, followed by Cruz at 34 percent, Kasich at 16 percent and Rubio at 11 percent.

CBS said the numbers suggest Cruz is “emerging more generally in the minds of many non-Trump voters as the alternative to the frontrunner.”

While an “overwhelming number” of Trump supporters described him as “authentic and not beholden to big donors,” backers also described him as “too extreme at times,” according to the poll.

On the Democratic side, frontrunner Hillary Clinton has a big lead in Florida over rival Vermont Sen. Bernie Sanders, 62-to-34 percent, according to the CBS poll.

However, she leads Sanders by single-digits in Ohio, 52-to-43 percent, the poll show. And Sanders has a narrow 48-46 percent lead in Illinois.

Early voting in Florida's primary comes to an end Sunday, with more than 1.9 million voters having already made their presidential choice.

Republican voters far outnumber Democratic ones, according to the latest figures released Sunday by the state Division of Elections.

Republicans account for more than 1.1 million early voters, while about 819,000 Democrats have cast ballots.

Early voters are projected to account for at least half the total number expected to vote in Tuesday's primary.

Florida's closed primary is open only to those registered to one of the major parties.

The Associated Press contributed to this report.