The Denver Post reported Obama was at 47 percent, Romney at 46 percent and 7 percent hadn't made up their minds. The poll has a 4 percentage-point margin of error.
The survey found voters under 50 are leaning toward Romney and those over 50 siding with the president, though within the margin of error.
Romney has a 47-42 edge among men; Obama a 48-42 lead among women. Those making less than $40,000 a year and those earning more than $80,000 support Obama, while those in the middle back Romney, the survey found.
Romney is finding supporters among gun owners, abortion opponents, military families and white voters, while Obama's support is stronger among those favoring access to abortion Latinos and those with college degrees.
Colorado voters see Romney as better-equipped to fix the economy, 47 percent to 44 percent, but Obama has a commanding 51-40 edge when those polled were asked which candidate is most in touch with the average working person.
Obama holds a 49-39 percent advantage in metropolitan Denver. Romney holds sway in the rest of Colorado 49-43, the poll shows.
The poll, conducted for the Post by SurveyUSA of New Jersey, surveyed 615 likely voters Sept. 9-12.