Donald TrumpDonald TrumpMcAuliffe takes tougher stance on Democrats in Washington Democrats troll Trump over Virginia governor's race Tom Glavine, Ric Flair, Doug Flutie to join Trump for Herschel Walker event MORE leads Ted CruzRafael (Ted) Edward CruzThe CDC's Title 42 order fuels racism and undermines public health Ocasio-Cortez goes indoor skydiving for her birthday GOP rallies around Manchin, Sinema 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 RubioRepublicans would need a promotion to be 'paper tigers' Defense & National Security — Military starts giving guidance on COVID-19 vaccine refusals Blinken pressed to fill empty post overseeing 'Havana syndrome' 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 CarsonBen CarsonRepublicans are the 21st-century Know-Nothing Party Sunday shows preview: Delta concerns prompt CDC mask update; bipartisan infrastructure bill to face challenges in Senate Government indoctrination, whether 'critical' or 'patriotic,' is wrong 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 PaulDemocrats fret as longshot candidates pull money, attention Journalist Dave Levinthal discusses 'uptick' in congressional stock trade violations McConnell vows GOP won't help raise debt ceiling in December after Schumer 'tantrum' 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.