‘‘And then on third down, he calls for a hail Mary, ending Medicare as we know it by giving seniors a voucher that leaves them to pay any additional cost out of their pockets. But there’s a flag on the play: Loss of up to an additional $6,400 a year for the same benefits you get now.’’

Romney denies that his plan to help the economy and reduce federal deficits will result in higher taxes for the middle class. But he has yet to provide enough detail to refute the claim, and Obama’s assertion rests on a study by the non-partisan Tax Policy Center.

As for the auto bailout that he backed and Romney opposed, Obama told the audience, ‘‘Three years later, the American auto industry has come roaring back. Nearly 250,000 new jobs.’’

Obama’s new campaign commercial said that under Romney’s ‘‘a middle class family will pay an average of up to $2,000 more a year taxes, while at the same time giving multimillionaires like himself a $250,000 tax cut.’’

Aides said it would air in Colorado, Iowa, New Hampshire, Nevada, Ohio and Virginia, the by-now familiar list of battleground states where the 2012 race for the White House is likely to be decided.

The president and aides have acknowledged for weeks that they and the groups supporting them are likely to be outspent by Romney, and recent figures say that has been the case in television advertising in the battleground states for much of the past two months.

Republican strategists contend that they have used the advantage to begin to erode Obama’s job favorability ratings, but declined to provide any polling results to support the assertion.

At the same time, reports by firms that track advertising show that Republicans hope to expand the campaign battleground into Wisconsin, Michigan and possibly Pennsylvania and Minnesota. An effective ad campaign there in such states could force Obama to divert resources from other states to defend turf he has long assumed would be his with relative ease.

Republicans ramped up their counter-programming as the opening of the Democrats’ convention approached.

‘‘People are not better off than they were four years ago. After another four years of this, who knows what it'll look like then,’’ said Republican vice presidential candidate Paul Ryan, campaigning in Greenville, N.C. ‘‘We’re not going to let that happen.’’ Obama’s top campaign surrogates had flinched from saying on Sunday that the average American is better off than four years ago, but they — and Biden — hastily recalibrated their response overnight.

‘‘You want to know whether we’re better off? I've got a little bumper sticker for you: ‘Osama bin Laden is dead and General Motors is alive,'’’ Biden told a campaign crowd in Detroit, the city that for generations has been synonymous with the American auto industry.

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