‘‘We can credibly meet the target the Bowles-Simpson Commission established of $4 trillion in deficit reduction’’ over a decade, he said.

Efforts to agree on a sweeping deficit-cutting deal with House Speaker John Boehner more than a year ago fell apart when liberals resisted measures Obama has accepted, including a gradual increase in the age of eligibility for Medicare to 67 from 65, and conservatives balked at the speaker’s willingness to include higher tax revenue in any agreement.

Nor did the president embrace the recommendations put together by the Bowles-Simpson Commission, a panel of outsiders that he appointed to recommend a solution to the nation’s long-running budget deadlock.

As for immigration, another issue that seems permanently gridlocked, the president said, ‘‘Should I win a second term, a big reason I will win a second term is because the Republican nominee and the Republican Party have so alienated the fastest-growing demographic group in the country, the Latino community.’’

It was a suggestion that Republicans will have to ease their opposition to measures giving illegal immigrants a path to permanent residence or citizenship if they lose the election.

Romney, in Reno, departed from previous campaign speeches and sought to personalize the choice voters face.

He ticked through several different hypothetical situations — a senior citizen struggling to pay for health care, a young family trying to educate their kids, an unemployed worker looking for a job — and insisted each would be better off under a Romney administration.

‘‘How many here identify with stories like that in your own home?’’ he asked, and hands shot up across the room.

‘‘This is an election about your family,’’ the Republican challenger said.

Romney running mate Paul Ryan was in Ohio, but not for a typical, late-campaign rally. Instead, in a speech at Cleveland State University, he said that in the nation’s long-running ‘‘war on poverty, poverty is winning.’’ He said community — the work done by churches, charities, friends and neighbors — is critical, although government, too, has a role in helping the disadvantaged.

‘‘There has to be a balance, allowing government to act for the common good, while leaving private groups free to do the work that only they can do,’’ he said.

Vice President Joe Biden, too, campaigned in Ohio, where he insisted that Republican protests notwithstanding, Romney and Ryan back a massive tax cut for the rich.

‘‘My mother said, Joey, if it looks like a duck and walks like a duck and quacks like a duck, it’s a duck. Man this is one quacking duck,’’ Biden said.

Obama did not mention the abortion controversy in Indiana, but his campaign spokeswoman did. Jennifer Psaki told reporters that the president finds Mourdock’s comments ‘‘outrageous and demeaning to women.’’

Nor did Romney mention the flap. Spokeswoman Andrea Saul said the campaign has not asked Mourdock to stop airing the endorsement TV ad Romney recorded.

There were echoes of the Republican National Convention in a new television commercial featuring Clint Eastwood and paid for by the super political action committee American Crossroads. A second term for the president would be a ‘‘rerun of the first, and our country just couldn’t survive that,’’ says the actor, who sharply criticized an imaginary Obama during a GOP convention speech to an empty chair.

Obama’s campaign unveiled a new 30-second ad reminding supporters of the dangers of complacency. Recalling the 2000 Florida recount that tipped the election to George W. Bush, the narrator says, ‘‘If you’re thinking your vote doesn’t count, that it won’t matter, well, back then, there were probably at least 537 people who felt the same way.’’ Images of war, economic hardships and the infamous hanging chads from disputed Florida ballots scroll by.

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Associated Press writers Kasie Hunt in Nevada, Philip Elliott and Matthew Daly in Ohio, Beth Fouhy in New York and Ken Thomas in Washington contributed to this story.

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