Donald TrumpDonald John TrumpSchiff pleads to Senate GOP: 'Right matters. And the truth matters.' Anita Hill to Iowa crowd: 'Statute of limitations' for Biden apology is 'up' Sen. Van Hollen releases documents from GAO investigation MORE leads Ted CruzRafael (Ted) Edward CruzDemocrats sharpen case on second day of arguments What to watch for on Day 3 of Senate impeachment trial Democrats' impeachment case lands with a thud with GOP — but real audience is voters MORE by 2 percentage points in a new poll from Iowa, suggesting a tightening presidential race ahead of the state’s Feb. 1 caucuses.

Trump leads the GOP field, with 31 percent support, in Quinnipiac University's new poll, followed closely by Cruz's 29 percent. That slim lead is within the poll’s 4-point margin of error.

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Voters view Cruz more favorably than they view Trump, however, and more are open to the possibility of voting for him, according to the new findings. 

This is only the third poll of the last 11 in Iowa in which Trump is on top, according to aggregation by RealClearPolitics. Other recent polls have shown Cruz in first place.

Trump in the last week has stepped up attacks on Cruz’s birthplace. Cruz was born in Canada, and Trump argues Democrats could make a case that he is not qualified to be president because he is not a natural born citizen.

Cruz was born to an American mother, and his campaign has argued he is qualified to be president just like 2008 GOP presidential nominee John McCain, who was born in the Panama Canal zone. Legal experts have long agreed that the Constitution's natural born citizen requirement includes those born to U.S. citizens outside the country.

In the poll, Cruz won more than one-third of the support of white, evangelical Republicans, an important constituency for him that typically makes up the majority of GOP caucusgoers. Trump attracted 27 percent with that group, and Marco RubioMarco Antonio RubioSenators press DHS over visa approval for Pensacola naval base shooter Lawmaker wants Chinese news outlet to register as foreign agent Apple under pressure to unlock Pensacola shooter's phones MORE received 13 percent, but other candidates won more than one-tenth of the evangelical vote.

Cruz outperformed Trump among people with college educations, with an income between $50,000 and $100,000, and who consider themselves very conservative. On the flip side, Trump did better among those without a college degree, and those making less than $50,000 and more than $100,000.

In the Quinnipiac poll, Rubio sits in third place, with 15 percent support, followed by Ben CarsonBenjamin (Ben) Solomon CarsonTrump administration ending delay on over B in Puerto Rico disaster aid HUD to roll back Obama-era housing desegregation rule Trump tells California, New York to 'politely' ask him for help with homeless population MORE, at 7 percent, and Chris Christie, at 4 percent. Jeb Bush has slipped to 3 percent, tied with Mike Huckabee, who won the caucuses in 2008. John Kasich and Rand PaulRandal (Rand) Howard PaulMarsha Blackburn shares what book she's reading during Trump Senate trial Sekulow indicates Trump should not attend impeachment trial Trump sets record for tweets as president on day House makes impeachment case MORE scored 2 percent; Carly Fiorina and Rick Santorum received 1 percent.

Quinnipiac surveyed 602 likely Republican caucusgoers in Iowa between Jan. 5 and Jan. 10.

Updated at 1:11 p.m.