Donald TrumpDonald John TrumpTillerson: Russia already looking to interfere in 2018 midterms Dems pick up deep-red legislative seat in Missouri Speier on Trump's desire for military parade: 'We have a Napoleon in the making' MORE leads Ted CruzRafael (Ted) Edward CruzSasse statement: Trump nominee who spread conspiracy theories has a ‘tinfoil hat’ Coalition of 44 groups calls for passage of drug pricing bill For the sake of our democracy, politicians must stop bickering 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 RubioTrump must send Russia powerful message through tougher actions McCain, Coons immigration bill sparks Trump backlash Taking a strong stance to protect election integrity 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 CarsonEPA to jumpstart 'war on lead' with strategy meeting Emails show Carson family involvement in HUD affairs: report Officials raised ethics concerns over Ben Carson's son assisting HUD event: report 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 PaulPentagon: War in Afghanistan will cost billion in 2018 Overnight Finance: Senators near two-year budget deal | Trump would 'love to see a shutdown' over immigration | Dow closes nearly 600 points higher after volatile day | Trade deficit at highest level since 2008 | Pawlenty leaving Wall Street group Rand Paul calls for punishment if Congress can't reach a long-term budget deal 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.