President Barack Obama has a significant lead on the Republican ticket of Mitt Romney and Paul Ryan in swing states on the issue of handling Medicare, according to a new Gallup poll out Monday.

Obama gets 50 percent of the vote on the question of which ticket voters "trust more to address the issues facing the Medicare system." Romney earns only 44 percent. Nationally, the gap is 2 percentage points larger.

The Gallup poll suggests that the campaign is having trouble winning over voters Ryan's budget plan, which proposes to make sweeping changes to Medicare.

Part of the reason for the disparity in the Gallup poll, in fact, is that more voters believe Obama has a "plan" for fixing the current Medicare system than do Romney and Ryan. Gallup attributes this to the difference in visibility between the Affordable Care Act — which makes significant reductions to Medicare spending — and Ryan's budget, which never passed the Senate.

The Medicare issue is an important one for most voters and one that Gallup says could help swing what remains a close election battle. Eighty-five percent of voters surveyed in a July Gallup poll said that ensuring the future viability of Social Security and Medicare was a very or extremely important issue for them in the upcoming election, which ranked as the fifth highest issue in the poll.

Despite voters' immediate preference for Obama on the issue, most of those surveyed are very pessimistic about both tickets. Only about a third of voters think either ticket would do much to strengthen Medicare.

Here's a look: