A cocksure and mocking President Barack Obama on Thursday gave one of his most sharply worded speeches in Miami this campaign season when he accused rival Mitt Romney of engaging in a dishonest “extreme makeover.”

“After running for more than a year in which he called himself ‘severely conservative,’ Mitt Romney’s trying to convince you that he was severely kidding,” Obama told a packed arena at the University of Miami.

Obama’s energy level, his zippy quotes and his pithy way of distilling his arguments stood in stark contrast with the president’s lethargic demeanor last week at a televised debate against Romney.

Obama’s performance was so lackluster that it’s costing him deeply in the polls. Obama has suggested that part of his bad performance was his shock at Romney’s capacity for reinvention.

Obama noted that Romney offered few specifics about what he would cut from the federal budget and said that the Republican wanted to reduce public-television subsidies that could target Big Bird.

The Romney campaign shot back with a written statement pointing out that Obama was ignoring the situation in Libya, where four foreign-service workers were killed after a Sept. 11 terrorist attack.

“Today, after his campaign said that the terrorist attack in Libya is only an issue because of Mitt Romney, the president hit the campaign trail and talked more about Big Bird than his failure to lead at home or abroad,” said Romney spokesman Ryan Williams.

“President Obama is obsessed with talking about a puppet rather than presenting a vision for a stronger foreign policy and a vibrant economy,” Williams said. “President Obama can continue to launch false attacks and focus on the small issues, but Mitt Romney will continue to address the serious issues confronting our nation and present his bold vision to grow our economy and keep American safe.”

But Obama said Romney isn’t talking boldly as much as he is dishonestly.

“He’s trying to go through an extreme makeover,” Obama said.

“And when he’s asked about the cost of his tax plan, he just pretends it doesn’t exist,” Obama said.

Sarcastically imitating Romney, Obama said: “What $5 trillion tax cut? I don’t know anything about a $5 trillion tax cut. Pay no attention to the $5 trillion tax cut — on my website.”

The crowd’s laughter interrupted him.

Obama’s remarks at UM’s BankUnited Center in Coral Gables — his fifth campaign stop in a row at a college — covered all of his administration’s high points: the death of Osama bin Laden, the end of Don’t Ask Don’t Tell, a drawdown of troops in Afghanistan and the end of the war in Iraq.

Obama never mentioned Election Day, Nov. 6.

Instead, the president repeatedly mentioned Oct. 27 as the day to vote. That’s the first day of Florida’s early in-person voting, when Democrats typically dominate.

When Obama first mentioned Romney’s name, the crowd of about 9,200 booed.

“Don’t boo, vote!” Obama said quickly.

The crowd exploded with applause.

By the end of the speech, Obama turned the phrase into a call and response.

Obama: “Don’t boo…”