A poll by The Denver Post, conducted Tuesday and Wednesday, put Romney 1 percentage point ahead of Obama, 48 percent to 47 percent. The poll of 614 likely voters has a 4 percentage-point margin of error.
The Post conducted a poll five weeks ago that found Obama with a 47-46 advantage.
"There is a relatively small number of individuals who are really undecided, and there's more of these people who are weakly decided," said Floyd Ciruli, a Denver pollster. "I think they tend to be more independent. They tend to be more moderate. They're definitely not attached to a candidate. They are able to move."
In Arizona, Obama is leading Romney 44 percent to 42 percent, CNN reported.
The state's two most populous counties, Maricopa and Pima, came out in support of Obama, while Romney has a lead in the rural counties.