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More than six in 10 Republican voters believe that, if no GOP presidential candidate wins a majority of delegates before the convention, the one with the most votes should be the party's nominee, according to a new national NBC News/Wall Street Journal poll.

That's compared with 33 percent of Republicans who say the nominee instead should be the candidate whom convention delegates think would be the party's best standard-bearer.

These numbers come as it's possible that Republican presidential frontrunner Donald Trump won't secure a majority of delegates once primary voting concludes on June 7, despite having won more votes, states and delegates than his Republican rivals.

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“I have millions of more votes than [Ted] Cruz, you know, if you add up the different primaries. Millions. And millions more than [John] Kasich,” Trump said recently in Pittsburgh.

But Cruz counters that those millions more votes won’t matter if Trump doesn’t have a majority of delegates. “If we go to a contested convention where nobody has a majority, it will be the delegates who were elected by the people who make the final decision,” he told NBC’s Chuck Todd last Thursday at the MSNBC town hall in Buffalo, N.Y. “But [the delegates] have been elected by the voters in the first place, and this is a battle to earn the support of the American voters across the country.”

The Republican National Committee says that the nominee is whomever secures a majority -- 1,237 -- of delegates at the Republican convention.

Asked about the poll result on NBC's Meet the Press Sunday, RNC head Reince Priebus noted that Trump has won a plurality - not a majority - of votes.

"If he was winning the majority of votes, he'd likely have the majority of delegates," Priebus said. "But that's not actually what's happening. He's winning a plurality of votes, and he has a plurality of delegates. And under the rules and under the concept of this country, a majority rules on everything."

According to the NBC/WSJ poll, 55 percent of Republican primary voters say it’s acceptable to them if Cruz wins the nomination by convincing the delegates from other candidates to support him.

Forty-five percent say it’s acceptable if Trump runs as independent if he’s denied the nomination, versus 47 percent who say it’s unacceptable.

Just 38 percent of Republicans say it’s acceptable if Trump goes into the Republican convention with the most delegates but does not become the nominee, versus 54 percent who say that outcome is unacceptable.

And only 20 percent say it’s acceptable if Republican delegates choose a nominee who has not run in the primaries, versus 71 percent who think that’s unacceptable.

The NBC/WSJ poll was conducted April 10-14 by both cell phone and landline interviews, and the sample here of 319 Republican primary voters has a margin of error of plus-minus 5.6 percentage points.