TAMPA, Fla. — With Mitt Romney’s selection of Representative Paul D. Ryan as his running mate, Florida quickly emerged on Monday as a critical test of the nationwide Republican gamble that concerns over the mounting federal debt can blunt potent Democratic attacks on conservative proposals to revamp Medicare.

As Mr. Romney campaigned through Florida on Monday, Democrats greeted him with a barrage of assaults, including a Web advertisement featuring worried elderly voters in this battleground state. The campaign took on a more heated air as President Obama suggested in Iowa that the Republican ticket would “end Medicare as we know it,” a warning echoed in North Carolina by Vice President Joseph R. Biden Jr.

Assailing proposed changes to the retiree health plan is a time-tested line of attack, nowhere more so than here in Florida, where voters 65 and older made up 22 percent of the electorate in the 2008 presidential election. Polls show that a majority of elderly voters nationally oppose changes in Medicare or Social Security, which Mr. Ryan in the past has also proposed altering.

The implications extend beyond Florida. Elderly voters are significant forces in Iowa, New Hampshire, Ohio, and Virginia and Pennsylvania, all states that could help determine the outcome of the election.