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

Donald TrumpDonald TrumpTrump to CNN reporter: 'That's a very rude question' Clinton: Trump 'would probably call' George Washington 'a loser' Clinton: Trump 'used undocumented workers' to build new luxury hotel 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.

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 CruzThe media is rigging the election by reporting WikiLeaks emails The Trail 2016: An important lesson in geography Webb: The race to 270 MORE (R-Texas) follows at 25 percent, Sen. Marco RubioMarco RubioUS abstains from UN resolution on Cuba embargo for first time Florida poll: Clinton leads Trump by 3 The media is rigging the election by reporting WikiLeaks emails 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.