Susan Page and Jenny Ung

USA TODAY

WASHINGTON — Donald Trump and Hillary Clinton expect to strengthen their claims on the presidential nominations in Tuesday's primaries, but a new USA TODAY/Suffolk University Poll underscores the serious challenges they face to heal divisions within their own parties.

Four in 10 Republicans surveyed aren't sure whether they'd vote for Trump if he's the nominee, saying they would consider instead supporting the other party's nominee or a third-party candidate or just staying home. Among Democrats, four in 10 supporters of Vermont Sen. Bernie Sanders say they aren't sure they would vote for Clinton.

If their candidate loses the nomination, voters in both parties split almost evenly over whether that would be because the winner prevailed fair and square — or because the system was rigged.

During primary battles, hard feelings aren't unusual. But in the GOP this year, opposition to Trump runs deep from some Republican leaders amid alarm about the billionaire businessman's off-the-cuff policy positions and provocative rhetoric. Among Democrats, Sanders has drawn bigger crowds and more fervent supporters than Clinton, particularly among younger voters.

And it's possible the challenges on both sides will last all the way to the national conventions this time.

Paleologos on the poll: Major challenges ahead for GOP

In past contests, nominees sometimes succeed in unifying party ranks, as Barack Obama did in 2008 after a pitched primary battle with Clinton, who then served as his secretary of State for four years. But the partisan wounds don't always heal. In 1992, divisions exacerbated by a conservative primary challenge to George H.W. Bush contributed to his defeat in November.

For Trump supporter Gregory Bullock, 35, of Phillipsburg, N.J., the question would be why Trump failed to get the nomination, if he did. "If it's something where the party rages against him — in other words, he goes to the convention with a majority but they derail him by strange methods — then I will not support whoever they appoint," he warns.

Sanders supporter Rachel Keller, 37, a homemaker from Dunedin, Fla., suspects the system is skewed. "It's been shown that the way this process works doesn't reflect what voters really want," she says. But Clinton supporter Maria Briscese, 54, of Bethel, Conn., disagrees. "Everyone knows the rules going in," she says.

If Clinton loses the nomination, most of her supporters say she would have been beaten fair and square. If Sanders loses the nomination, most of his supporters say it would be because the system was unfairly stacked against him.

The poll of 1,000 likely voters, taken by landline and cellphone Wednesday through Sunday, has a margin of error of +/- 3 percentage points. The margin of error for the sample of 363 likely Democratic voters is +/-5.1 points. For the sample of 292 likely Republican voters, it's +/-5.7 points.

Sanders narrows gap

While Clinton is on course to win the 2,383 delegates needed for nomination at the Democratic convention in Philadelphia, she has seen her double-digit lead in the USA TODAY survey two months ago narrow to within the margin of error. Now Clinton is supported by 50% and Sanders by 45%, compared with her 10-point lead in the February poll.

And while Trump has a narrow path to command the 1,237 delegates needed at the Republican convention in Cleveland, he maintains a muscular edge over Texas Sen. Ted Cruz and Ohio Gov. John Kasich in the poll. Trump is backed by 45%, Cruz by 29% and Kasich by 17%.

As the GOP field has narrowed, support for all three remaining contenders has grown: Trump and Kasich by 10 points, Cruz by 9. The assertion by some that Trump couldn't win a share of the support from establishment candidates who dropped out, including Florida Sen. Marco Rubio and former Florida governor Jeb Bush, hasn't turned out to be true.

Meanwhile, in the wake of double-digit victories in the New York primary last week, Trump and Clinton are poised for more good news from the primaries Tuesday in five states along the Amtrak corridor: Connecticut, Delaware, Maryland, Pennsylvania and Rhode Island. Statewide polls give Trump double-digit leads in all of them, and Clinton wide leads in Maryland and Pennsylvania. She has narrow leads in the three smaller states.

Still, Sanders finds himself on solid ground among Democrats on some issues. Even if Clinton clinches the nomination, 54% of likely Democratic voters say he should continue his campaign until the convention, no matter what. That includes not only seven in 10 of his supporters but also four in 10 of her backers.

Democrats also share Sanders' skepticism about the proper role of superdelegates, the elected and party officials who are unpledged delegates to the convention. Sixty percent of Democrats, including a majority of Clinton supporters, say the nominee should be the candidate who wins the most pledged delegates. Only one in four say superdelegates should have a vote.

And there's this: 61% of Sanders supporters say if he isn't nominated, Clinton should put him on the ticket as the vice presidential nominee. That includes a majority of Clinton supporters. "It would be awesome," says Keller. "That way everyone's voice can be represented. But we all know that's not how politics really works."

Neither Clinton nor Sanders' campaign officials see a joint ticket as likely.

Elections 2016 | USA TODAY Network

Republican rules

When it comes to the Republican convention, views of the rules seem to be shaped by which candidate a voter supports. Seven of 10 Trump backers say a candidate with who has clear lead in delegates, even if it's not a majority, should be nominated — an argument Trump has been making.

Just one in four of those supporting Cruz or Kasich share that view. Late Sunday, the two campaigns announced an alliance aimed at blocking Trump from winning a delegate majority. Kasich will defer to Cruz in the Indiana primary May 3, and Cruz will defer to Kasich in the Oregon and New Mexico contests that follow.

"With major divides in both parties looming, we are in a transition away from intra-party differences on taxes, ISIS, Wall Street, or building a wall," says David Paleologos, director of the Political Research Center at Suffolk University. "Now, voters are fixed on the power of delegates, the nominating conventions, and whether the system is unfairly stacked against outsider candidates like Trump and Sanders."

On one issue, Republicans broadly agree: no white knights. By more than 3-1, 67%-20%, they say the convention should only consider candidates who ran for the nomination this year. There's little appetite for turning to someone such as House Speaker Paul Ryan to win the party's bid over those who have been battling for it for a year.

November showdowns

In general-election matchups, Clinton would defeat Trump by double digits — and Sanders would beat him by more.

At the moment, Clinton leads Trump, 50%-39%; Sanders leads him 52%-37%. Clinton leads Cruz, 49%-42%. The edge for Sanders over Cruz is wider, 50%-38%.

Among the Republicans, only Kasich would defeat Clinton, 46%-41%. A Sanders-Kasich race would be close, 44%-43%.

Regardless of which candidate they support, 50% of those surveyed say Clinton is the most likely victor in November, almost double the 26% who predict Trump will win the White House.

"I'm voting for her because she has a lot of experience," says Janice Neal, 69, who lives in rural Missouri. "She's been through a lot in her life and she has learned a lot and been very tough because of it."

Kenneth Mays, 62, a retiree from Winston-Salem, N.C., backs Trump. "I look at the United States realistically as a giant corporation," he says. "It's a big industry, and Donald Trump has that experience in running big industries." Mays hopes to vote for Trump on the Republican ticket. But if Trump loses the nomination and makes an independent bid, Mays, like 56% of all Trump supporters, says he still would vote for him.

Trump, favored in five states Tuesday, now faces Cruz-Kasich alliance

Former Sanders adversary: Vt. senator will eventually back Clinton