The Mayors Against Illegal Guns survey of voters in Virginia, North Carolina and Colorado indicated 45 percent of voters trusted Obama on gun issues, while 40 percent trusted Romney, results released Thursday indicated.
The three-state survey, paid for by Mayors Against Illegal Guns, also found the National Rifle Association had little impact on the presidential election.
Mark Glaze, director of Mayors Against Illegal Guns, said the survey and conversations in Washington indicate the perceived power of the NRA is slipping, Politico reported.
"Members of Congress will tell you privately that they agree we need stronger gun laws, but they run scared from the perceived power of the gun lobby," Glaze said. "There is a growing pile of evidence the NRA has built a mythology around their ability to swing elections that has little basis in fact."
Results indicated Obama had the largest advantage in Virginia, where he led his Republican rival 48 percent to 39 percent. In Colorado, Obama's edge was 44 percent to 40 percent for Romney and in North Carolina Obama had 42 percent to Romney's 41 percent.
The poll also found 27 percent of Colorado voters recalled being aware of the NRA's stance in the election while 26 percent heard from the NRA in Virginia and 22 percent expressed the same in North Carolina.
The Sunlight Foundation reported two NRA groups spent at least $12 million opposing Obama and supporting Romney.
In all three states, at least 88 percent said they favored background checks for all gun purchases, results indicated. Majorities also said they backed laws that would bar convicted sex offenders or domestic abusers from carrying concealed guns across state lines.
Results of the poll, conducted by Democratic pollster Momentum Analysis and GOP polling group Chesapeake Beach Consulting, are based on telephone interviews with 500 voters in each state Nov. 7-8. The margin of error is 4.4 percentage points.