Poll: Trump loses head-to-head vs. both Cruz, Rubio

Donald TrumpDonald TrumpTrump to undo Obama's climate change agenda Kushner met Russian bank executives: report Trump tweets: 'Trump Russia story is a hoax' MORE’s national lead in the GOP presidential primary is shrinking, and he loses head-to-head match-ups with his two closest opponents, according to a poll out Tuesday morning.

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Thirty-four percent of registered Republican and GOP-leaning independent voters say they want Trump to win the GOP nomination in a new ABC News/Washington Post survey.

Sen. Ted CruzTed CruzConservatism's worst enemy? The Freedom Caucus. Republicans giving Univision the cold shoulder: report How 'Big Pharma' stifles pharmaceutical innovation MORE (R-Texas) follows at 25 percent, Sen. Marco RubioMarco RubioRepublicans giving Univision the cold shoulder: report Week ahead: Senate panel to vote on Trump's Labor pick Senators introduce new Iran sanctions MORE (R-Fla.) at 18 percent and Ohio Gov. John Kasich at 13 percent in the national poll, representing increases of 4, 7 and 11 points in the survey since January, respectively.

But in hypothetical one-on-one match-ups with Cruz and Rubio, Trump loses. Cruz leads Trump 54 to 41 percent, and Rubio leads the outspoken businessman 51 to 45 percent.

Cruz trounces Trump among both evangelicals (64 percent to 31 percent) and self-identified very conservative voters (60 to 34 percent). Rubio also beats Trump among both groups, though by far smaller margins.

Favorability among GOP women could be a hurdle for Trump.

Just about a quarter of women support him, 24 percent, compared to 44 percent of men surveyed. Those figures have fluctuated in recent months.

Six in 10 Republican and GOP-leaning women, 60 percent, say they'd be dissatisfied with Trump as the Republican nominee, compared to 35 percent of men.

The results of the poll come as Trump's rivals battle to keep him below the necessary 1,237-delegate threshold required to lock up the Republican nomination, forcing a brokered convention in July.

Four states are holding voting on Tuesday, including Michigan, where polls have shown a tightening race. Kasich and Rubio are also fighting to win their home states of Ohio and Florida next week in winner-take-all contests.

The survey of 1,000 adults overall was conducted March 3–6 via landlines and cellphones with a margin of error of 5.5 percentage points.