The Republican National Committee is sticking with its forecast that the party is likely to have a presidential nominee settled before the convention in Cleveland in July, with a top spokesman putting those odds at 85 percent Monday.

“I still believe that we’re at 85 percent certainty that we will have a nominee going into that convention,” RNC spokesman Sean Spicer said on CNN’s “New Day.”

Fresh off wins in Louisiana and Kentucky over the weekend, Republican front-runner Donald Trump has accumulated 384 delegates in the 2016 GOP race to Sen. Ted Cruz’s 300, Sen. Marco Rubio’s 151 and Ohio Gov. John Kasich’s 37, according to the latest tally from the AP.

Mr. Cruz picked up wins in Kansas and Maine on Saturday, while Mr. Rubio won Puerto Rico on Sunday. Mr. Kasich has yet to win a state. A candidate needs to secure 1,237 delegates to clinch the nomination.

Voters in Hawaii, Idaho, Michigan and Mississippi head to the polls on Tuesday, when a total of 150 delegates are up for grabs.

Some Republicans determined to stop Mr. Trump from securing the nomination are hoping, contra Mr. Spicer’s prediction, that denying him victories in winner-take-all states like Ohio and Florida on March 15 could mean nobody reaches 1,237 delegates by Cleveland, even if the support ends up divided among the other three candidates.

Former Massachusetts Gov. Mitt Romney, the party’s 2012 GOP nominee, has chimed in on the race recently, saying a contested convention isn’t out of the question, and suggesting, for example, that voters support Mr. Rubio in Florida and Mr. Kasich in Ohio if they have designs on stopping Mr. Trump.

Mr. Cruz, meanwhile, has warned GOP leaders about the prospect of a contested convention, saying there would be a “revolt” and that voters should be the ones to ensure Mr. Trump is defeated.

Mr. Spicer did acknowledge that the process is still likely to take a while, saying that even if a candidate won every single delegate going forward, nobody could reach the 1,237 required to be the nominee until April 26.

“So we basically guarantee that we won’t have a nominee right now until May,” he said.

Mr. Trump is looking to hold onto his lead, while the rest of the field is hoping that a blitz of anti-Trump ads by groups like the Club for Growth will dent his seeming invincibility in the upcoming contests.

Mr. Trump appears to have the edge in Michigan, where 59 total delegates are at stake Tuesday, leading with 36 percent support in a Monmouth University Poll out Monday. He was ahead of Mr. Cruz, at 23 percent, Mr. Kasich at 21 percent, and Mr. Rubio of Florida at 13 percent.

But the poll, which was taken from Thursday to Sunday, also showed Mr. Kasich within 6 points of Mr. Trump among interviews in the survey’s final two days, indicating the billionaire businessman’s lead in the state might not be insurmountable.

“After this past weekend’s mixed bag of results, Trump appears positioned for a win in Michigan, but the race may be tightening in the final hours,” said Patrick Murray, director of the independent Monmouth University Polling Institute.

A Monmouth poll on Florida released Monday also showed Mr. Trump’s lead over Mr. Rubio shrinking, now just 8 percentage points after having held double-digit leads in the state in other recent polls.

And a survey released Monday by the Democratic-leaning firm Public Policy Polling gave Mr. Trump a mere 3-point edge in Ohio, receiving 38 percent to Mr. Kasich’s 35 percent.

Both Mr. Kasich and Mr. Rubio have vowed to win their respective home states, which both vote on March 15.

Mr. Kasich has said he’ll likely exit the race if he doesn’t win Ohio. Mr. Rubio has not made such a declaration about Florida, but a loss there would deal a near-fatal blow to the senator’s campaign and could solidify Mr. Cruz as the alternative to Mr. Trump in the race.

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