Real estate mogul Donald Trump leads the 2016 GOP pack but faces problems with the broader electorate, according to a new poll that found half of U.S. voters would be embarrassed to have Mr. Trump as president and showed Mr. Trump trailing the two leading Democratic contenders.

Mr. Trump led the 2016 GOP presidential field at 28 percent in the national Quinnipiac poll released Tuesday, followed by Sen. Ted Cruz of Texas at 24 percent, Sen. Marco Rubio of Florida at 12 percent, retired neurosurgeon Ben Carson at 10 percent and New Jersey Gov. Chris Christie at 6 percent.

Among registered voters overall, though, 50 percent said they would be embarrassed to have Mr. Trump as president, 23 percent said they would be proud, and 24 percent said they wouldn’t feel either way. Fifty-three percent of voters overall said they don’t think he has a good chance of winning in the general election next November.

“Half of American voters say they’d be embarrassed to have Donald Trump as their commander in chief and most Americans think he doesn’t have a good chance in November, but there he is still at the top of the Republican heap,” said Tim Malloy, assistant director of the Quinnipiac University Poll.

On the Democratic side, former Secretary of State Hillary Clinton had a 31-point, 61 percent to 30 percent, lead over Sen. Bernard Sanders of Vermont, with former Maryland Gov. Martin O’Malley at 2 percent.

In head-to-head match-ups, Mrs. Clinton led Mr. Trump by 7 points, 47 percent to 40 percent, and Mr. Sanders led Mr. Trump by 13 points, 51 percent to 38 percent.

Thirty-five percent of voters overall said they would be embarrassed to have Mrs. Clinton as president, 33 percent said they would be proud, and 29 percent said neither.

“Hillary Clinton tops him. Sen. Bernie Sanders hammers him, and Sen. Ted Cruz is snapping at his heels. Can a candidate that half the American electorate thinks is an embarrassment win in November?” Mr. Malloy said.

Overall, 59 percent said Mrs. Clinton would have a good chance of beating the 2016 GOP nominee next November. She led Mr. Rubio by 1 point in a head-to-head match-up, 44 percent to 43 percent, and was tied with Mr. Cruz at 44 percent apiece.

Fifty-three percent of voters did say Mr. Trump would do a better job handling the economy, compared to 43 percent for Mrs. Clinton. But 48 percent said Mrs. Clinton would do a better job handling terrorism, compared to 45 percent for Mr. Trump.

Mr. Trump had a positive 63 percent favorability rating among Republicans, with 30 percent reporting an unfavorable opinion of him.

But he had a negative 33 percent/59 percent favorable/unfavorable split among overall voters - the second-worst net score behind former Florida Gov. Jeb Bush, who had a 28 percent/56 percent split.

Mr. Bush also had the worst net split among Republicans, with 37 percent reporting a favorable opinion and 52 percent reporting an unfavorable opinion.

Mrs. Clinton had a negative 43 percent/51 percent favorable/unfavorable split among overall voters, but a positive 82 percent/13 split among Democrats.

Mr. Cruz had the best rating among Republican voters, with 68 percent reporting a favorable opinion and 7 percent reporting an unfavorable one. Forty percent of Republicans who watched or listened to the last GOP debate also said Mr. Cruz did the best job, followed by Mr. Trump at 20 percent.

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