CHARLOTTE — Former president Bill Clinton, in a fiery nominating speech Wednesday at the Democratic National Convention, mixed passion, policy detail, and humor with an urgent plea for Americans to stay the course with President Obama, who made a surprise appearance by joining Clinton on stage after his speech.

Following a booming welcome from 20,000 delegates and guests, Clinton turned the tables on a familiar Republican critique of the president — that the country is worse off than in 2008 — by making a forceful argument that the reverse is true.

“In Tampa, the Republican argument against the president’s reelection was actually pretty simple — pretty snappy. It went something like this: We left him a total mess. He hasn’t cleaned it up fast enough. So fire him and put us back in,” said Clinton, whose speech followed Massachusetts Senate candidate Elizabeth Warren’s.

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“I like the argument for President Obama’s reelection a lot better. Here it is. He inherited a deeply damaged economy. He put a floor under the crash. He began the long, hard road to recovery and laid the foundation for a modern, more well- balanced economy that will produce millions of good new jobs, vibrant new businesses, and lots of new wealth for innovators,” Clinton said.

For nearly 50 minutes, Clinton played the crowd like a folksy, charismatic professor, dissecting and criticizing Republican plans on items such as Medicare, debt reduction, and defense spending in ways that had the crowd alternating between laughter, cheers, and riveted silence.

“We’ll be deciding what kind of country we want to live in,” Clinton said. “If you want a winner-take-all, you’re-on-your-own society, you should support the Republican ticket. But if you want a country of shared opportunities and shared responsibility, a we’re-all-in-this-together society, you should vote for Barack Obama and Joe Biden.”

After Clinton finished his speech, Obama strode into the stage and wrapped his arms around Clinton to a thunderous, swelling, standing ovation. Then the convention began the roll call that resulted in Obama’s formal nomination to a second term.

Warren, who received prime-time billing just before Clinton, argued for greater economic fairness, a theme she has made a centerpiece of her Massachusetts campaign against Senator Scott Brown, a Republican.

Warren recalled her upbringing “on the ragged edge of the middle class” and highlighted her belief that middle-income Americans have been “chipped, squeezed, and hammered.”

“People feel like the system is rigged against them,” Warren said. “And here’s the painful part: They’re right. The system is rigged.”

Response from the Romney camp was immediate. His spokesman, Ryan Williams, said, “President Clinton drew a stark contrast between himself and President Obama tonight. Bill Clinton worked with Republicans, balanced the budget, and after four years he could say you were better off. Barack Obama hasn’t worked across the aisle — he’s barely worked with other Democrats.”

In addition to concern about the fate of social programs, Democrats have opted to counterpunch against Republican criticism of the balky economy with the argument that the country has experienced steady, incremental progress under the president.

They also hammered Romney with the now-familiar critique that Bain Capital, his private-equity business, had cost some workers their jobs in the company’s pursuit of profits.

Nancy Pelosi, the House minority leader and former speaker, called for perseverance despite the obstacles.

“This year, we are determined to re-elect an extraordinary president who, in no ordinary time, led America back from the brink of depression — while Republicans tried to block him at every turn,” Pelosi said. “This election offers the clearest choice of our time.”

US Representative Steny Hoyer of Maryland, the House minority whip, lambasted Republicans for working to sabotage the president rather than seeking a bipartisan plan to aid the country.

Turning the tables on Republican questions about a nation they see in decline, Hoyer — citing 1 million jobs added during the president’s term — said to cheers: “Surely, Mr. Romney thinks we’re better off today than we were then.”

Sister Simone Campbell, the leader of a cross-country protest against proposed GOP budget cuts called Nuns on the Bus, reiterated her criticism of the Republican vision, which she said would cripple social services for low-income families.

Earlier in the evening, when Time Warner Cable Arena was half full, the delegates were challenged with deciphering the thick Boston diction of Mayor Thomas M. Menino, who described Romney as a nice guy who fell short as governor of Massachusetts.

“Mitt Romney, he may come from Boston, but his campaign values aren’t Boston values,” Menino said. “We know this country didn’t become great by excluding others. . . . In Boston, you know what we call immigrants? Mom and Dad. You know what we call same-sex couples? Our friends, our brothers, and our sisters.”

The mayor spoke of his working relationship with Romney.

“He made a lot of decisions that were bad for our state, and now he wants to carry those wrong-headed policies to the rest of our country,” Menino said. “I like Mitt Romney, but he’s learned all the wrong lessons, and now he’s doubling down on all the wrong plans.”

Obama arrived here on Air Force One on Wednesday, preparing to accept the party’s nomination for reelection as he put the finishing touches on a speech he will deliver Thursday night in the convention hall.

He is expected to praise the accomplishments of his administration — health care reform, financial regulation, the auto bailout, and ending the war in Iraq — and underline his differences with Romney and Ryan, who he said will slash social services like Medicare and shred the safety net for the poor and middle class.

The president had been scheduled to deliver the speech in Bank of America Stadium, a 74,000-seat outdoor arena that would have rekindled powerful memories of his acceptance speech four years ago at a packed football stadium in Denver. Now, he is set to appear inside 20,000-seat Time Warner Cable Arena, which has hosted the first two days of the convention.

Convention organizers said that weather pushed them indoors — there is a chance of rain on Thursday — but Republicans speculated that Obama would have trouble filling the stadium. Regardless, the change means that far fewer people will be able to hear Obama’s speech in person, and many volunteers who had been promised a seat now will be turned away.

Obama was planning to hold a conference call on Thursday afternoon for ticket holders who will not be able to attend in person.

Obama also faces a challenge to strike the right note, observers said.

“He needs to be more African-American pulpit than professorial,” said Doug Brinkley, an author and presidential historian at Rice University. “Meaning, really generate a kind of emotion from the audience. But he also has to hit these somber tones about what it means to be commander-in-chief vis-a-vis our troops and understanding the costs of poverty in the country.”

Brinkley said he was told that Obama speechwriters had been studying Franklin Delano Roosevelt’s speech in 1936, when he tried to reassure the country while running for reelection during the Great Depression.

Romney remained in Vermont on Wednesday, holed up in the home of his former lieutenant governor, Kerry Healey, as he worked with top aides on debate preparations.

On Friday, Romney is scheduled to attend a morning rally in Orange City, Iowa, and an evening one at Holman Stadium in Nashua. President Obama, Michelle Obama, Vice President Joe Biden, and his wife, Jill, will hold a morning rally in Portsmouth, N.H., and an evening rally in Iowa City, Iowa.