Wooing Florida voters, President Barack Obama warned Thursday that Republican challenger Mitt Romney would gut his health care reform law and turn Medicare into a voucher program, driving up costs for the elderly on fixed incomes. Romney, firing away near his Boston home base, accused Obama of caring only about saving his own job — not the jobs of Americans.

In the daily war of words in an up-for-grabs presidential contest, health care politics took top billing as Obama opened two days of campaigning in Florida, the largest and most coveted of the nation’s Election Day toss-up states. Obama could see his chances for another term seriously damaged if Romney prevails here.

For his part, Romney, in hastily arranged remarks to reporters near Boston, kept the focus on the sluggish economic recovery under Obama’s watch. He cited new government figures showing that the number of American seeking unemployment benefits rose by 34,000 last week, a figure that may have been skewed higher by seasonal factors.

Both candidates were pouring most of their money and attention into the collection of fewer than 10 states expected to decide the election. First lady Michelle Obama launched a new effort to rally supporters behind her husband, trying to light a fire by saying the whole race could “come down to just a few votes per precinct in key states.’’

Nowhere is the campaign potentially more pivotal than in Florida, which decided the 2000 election and remains the ultimate swing state. With a large pool of retired voters, Medicare has been used by both parties to rally support from seniors in Florida and elsewhere, mostly by warning that the other party had in mind changes that would curb the national insurance program for older Americans.