TAMPA, Fla. — Former Massachusetts Gov. Mitt Romney swept to the Republican presidential nomination Tuesday night, praised lovingly by his wife from the stage as the “man American needs” and cheered by a hall packed with convention delegates eager to propel him into the fall campaign against President Barack Obama.

“This man will not fail. This man will not let us down,” Romney said in a prime-time speech that sounded at times like a heart-to-heart talk among women and at times like a testimonial to her husband.

“It’s the moms who always have to work harder, to make everything right,” she said, and she vouched firmly for her husband: “You can trust Mitt. He loves America.”

New Jersey put him over the top in a ritual roll call of the states. New Jersey’s governor, Chris Christie, had the difficult job of following Mrs. Romney before the cheering crowd.

Christie, the convention keynoter, said, “It’s time to end this era of absentee leadership in the Oval Office and send real leaders to the White House.”

The opening session passed up no opportunity to broaden Romney’s appeal. Speakers included Hispanic candidates for office, former Rep. Artur Davis, a former Democrat and member of the Congressional Black Caucus, businessmen and women and former Sen. Rick Santorum of Pennsylvania, Romney’s most persistent, conservative nemesis in the nominating campaign.

To send Romney and ticketmate Paul Ryan into the fall campaign, the convention quickly approved a conservative platform that calls for tax cuts — not government spending — to stimulate the economy at a time of sluggish growth and 8.3 percent unemployment.

Texas Rep. Ron Paul, who never won a primary or caucus, drew several dozen delegate votes. Earlier, his supporters chanted and booed after the convention adopted rules they opposed, but were powerless to block, to prevent those votes from being officially registered.

Several members of the Maine delegation walked out of the arena after the convention affirmed the GOP’s decision to replace 10 of the state’s 24 delegates.

Romney opposes abortions, except in cases of rape, incest, or when “the health and life of the mother” are at stake, he said in a convention week interview.

Obama, who accepts renomination at the Democratic National Convention in Charlotte, N.C., next week, campaigned in Iowa Tuesday as he set out on a tour of college campuses in battleground states in hopes of boosting voter registration among college students.

Before departing the White House, he made a point of appearing before reporters to announce the government’s latest steps to help those in the way of Isaac. He signed a declaration of emergency for Mississippi and ordered federal aid to supplement state and local storm response efforts in the state.

His surrogates did their best to counter Romney and the Republicans.

Los Angeles Mayor Antonio Villaraigosa, dismissing GOP attempts to woo Hispanic voters, said, “You can’t just trot out a brown face or a Spanish surname and expect people are going to vote for your party or your candidate.” He added, “This is a party with a platform that calls for the self-deportation of 11 million people.”

Hispanics strongly favor Obama, according to public polls, and Romney and his party have been seeking to win a bigger share of their votes by emphasizing proposals to fix the economy rather than ease their positions on immigration.

Female voters, too, prefer the president over his challenger, and Democrats have done their best to emphasize GOP opposition to abortion and even suggest the party might try and curtail access to contraceptives if it wins power.

Whatever the impact of those issues, the polls show the economy is overwhelmingly the dominant issue in the race, and on that, the voters narrowly say they trust Romney more.

In an AP-GfK poll taken Aug. 16-20, some 48 percent of registered voters said they trust Romney more on economic issues, to 44 percent for Obama.

However, a Washington Post-ABC News in the days immediately before the convention found that 61 percent of registered voters said Obama was more likable, and 27 percent said Romney.

The convention took place in an atmosphere of security that was both stringent and selective. Thousands of police from all over the country, joined by National Guard troops, Secret Service and others, stood in small groups at checkpoints, demanding those entering a secure area display proper credentials numerous times.

But former Michigan Gov. John Engler and an aide were hustled to the front of a long line waiting to clear security at one building.

Aside from Paul, Romney’s long-ago rivals for the party nomination had bit roles at his convention, if that.

Michele Bachmann and Herman Cain posed for a photo after running into each other at the convention center. Newt Gingrich and Rick Santorum were also in town, as well, both with speaking slots, unlike Bachmann and Cain.

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Associated Press writers Brian Bakst, Thomas Beaumont, Tamara Lush, Brendan Farrington, Julie Mazziotta, Steve Peoples, Kasie Hunt and Philip Elliott in Florida and Steven Ohlemacher, Alicia A. Caldwell and Jennifer Agiesta in Washington contributed to this re