The survey found 50 percent of voters say Obama is more trustworthy on the issue, while 44 percent pick Romney. The poll also found more than half, 53 percent, do not believe Medicare will be providing adequate coverage to those over 65 in 20 years while 44 percent are optimistic.
The Romney campaign has been blasting Obama on Medicare. Both Republican vice presidential nominee Paul Ryan and Obama addressed the American Association of Retired Persons conference in New Orleans Friday, with Ryan repeating his charge that Obama was taking money from Medicare to fund the Affordable Care Act.
Obama is attacking Ryan's plan, part of a proposed massive overhaul of the federal spending and taxes, to convert Medicare to a voucher system for future recipients.
Voters over 65, who polls indicate are most likely to support Romney, find him more trustworthy on Medicare 50 percent to 41 percent. But voters under 30, Obama's strongest group, trust him 67-25.
The poll was conducted Sept. 11-Sept. 17 in Colorado, Florida, Iowa, Michigan, Nevada, New Hampshire, New Mexico, North Carolina, Ohio, Pennsylvania, Virginia and Wisconsin. Gallup surveyed 1,096 registered voters.
The margin of error is 4 percentage points.