A poll released Tuesday shows Gov. John Kasich is trailing Donald Trump in Ohio, raising the stakes for Mr. Kasich’s long-shot quest to grab the GOP presidential nomination when the convention comes to Cleveland in July.

The Quinnipiac University Poll showed Mr. Trump supported by 31 percent of Ohio Republican likely voters in the March 15 primary and 26 percent for Mr. Kasich.

They’re followed by Sen. Ted Cruz of Texas with 21 percent, Sen. Marco Rubio of Florida at 13 percent, and Dr. Ben Carson with 5 percent. Five percent are undecided.

On the Democratic side, the poll shows former Secretary of State Hillary Clinton leads Sen. Bernie Sanders of Vermont 55 percent to 40 percent among likely primary voters.

Mr. Trump also boasts the most solid support in Ohio, with 78 percent saying they won’t change their minds, compared with 50 percent of Kasich supporters.

Peter Brown, assistant director of the Quinnipiac University Poll, said Mr. Kasich winning Ohio is crucial to denying Mr. Trump the nomination. Ohio is a winner-take-all state, so whoever emerges with the most votes gets all 66 delegates.

“Five points is not an insurmountable lead,” Mr. Brown said. “These numbers aren’t terrible for Kasich. And one assumes the governor’s ground game in Ohio will be better than Trump’s. But we will find out.”

Mr. Kasich is endorsed by the Ohio Republican Party, so in effect, he has a field operation with 88 county offices.

“We are very comfortable with the governor’s strong position and his strong organization at home,” Kasich spokesman Rob Nichols said.

After Mr. Kasich’s fifth- place showing in the South Carolina primary on Saturday, pressure is rising on Mr. Kasich to bow out in support of Mr. Rubio and possibly improve his chances of being the vice-presidential nominee.

Mr. Kasich said Tuesday it is the other candidates who should bow out.

“I’ve spent the least amount of money and am rising in the polls. I can win my home state. Why would I clear the decks for them? They ought to be consolidating around me,” he said, according to the Columbus Dispatch.

“Everybody is getting slaughtered in their state, and we’re within the margin of error,” Mr. Kasich said. “We’re going to win Ohio, there’s no question about it. ... The last thing I worry about is how we’re going to do in Ohio. We’re going to win Ohio.”

Coming up on March 1, the so-called SEC Primary, are 13 states where Mr. Kasich, with his modest war chest, has been able to campaign in Massachusetts, Virginia, and Georgia.

Kasich strategist John Weaver issued a memo in which he argued that the governor’s position is more solid than Mr. Rubio’s.

He said if Mr. Rubio ends the March 1 round of primaries without a delegate lead, then his campaign will be over because the rest of the primary states are less favorable to him, including his own state. Florida votes the same day as Ohio.

“As the campaign moves to the bigger, Midwestern states, the Kasich campaign will be able to take advantage,” Mr. Weaver said.

Jordan Russell, the Ohio campaign spokesman for Mr. Rubio, fired back.

“Marco is the only candidate in the race who can unite the party and defeat Hillary Clinton in the general election. We are running a strong 50-state campaign and will compete everywhere,” Mr. Russell said.

According to the Quinnipiac poll, Mr. Kasich has the best favorability rating, at 77 percent, among the Republican voters in Ohio, followed by Mr. Rubio with 62 percent, Mr. Cruz with 60 percent, and Mr. Trump at 57 percent.

In a Quinnipiac survey in October, Mr. Trump had 23 percent compared with Mr. Kasich’s 13 percent. Dr. Carson had 18 percent.

On the Democratic side, Mrs. Clinton and Mr. Sanders have favorability ratings of 77 percent among Democratic voters, with Mrs. Clinton viewed unfavorably by 17 percent and Mr. Sanders by 11 percent.

Quinnipiac interviewed 759 likely Republican voters and 518 Democratic voters Feb. 16-20. The poll has a margin of error of plus or minus 3.6 percentage points for Republicans and 4.3 points for Democrats.

Contact Tom Troy: tomtroy@theblade.com or 419-724-6058 or on Twitter @TomFTroy.

First Published February 24, 2016, 5:00 a.m.