The Quinnipiac University poll found that 45 percent of respondents said they would vote for Udall, and 44 percent for his Republican challenger, Rep. Cory Gardner, making the race too close to call.
Udall, a member of one of the most prominent western political families, won the Senate seat in 2008 with 53 percent of the vote.
The poll also matched Hillary Clinton, considered a likely candidate for the Democratic presidential nomination in 2016, against a number of Republicans. Sen. Rand Paul, R-Ky., would defeat Clinton in Colorado 48-43, while Clinton would split the vote 42-42 against New Jersey Gov. Chris Christie, beat former Florida Gov. Jeb Bush 45-40, and have a slight 45-44 edge over former Arkansas Gov. Mike Huckabee.
Asked to name the issue most important to them, 16 percent of respondents said the economy and 14 percent said healthcare, with every other issue running far behind. That is bad news for Udall because Gardner has a 53-40 percent edge among those concerned with the economy, and 57-36 percent among those who said healthcare is the big issue.
Udall has a big lead among female voters, while Gardner leads with men. Gardner has a small lead among independent voters.
Quinnipiac in Hamden, Conn., surveyed 1,298 registered voters between April 15 and April 21. The poll has a margin of error of 2.7 percentage points for the entire sample.