TAMPA, Fla. -- Florida Sen. Marco Rubio, the son of Cuban immigrants who became one of the Republican Party's rising stars, offered his own life story, and that of Mitt Romney, as testament to the exceptional nature of America on Thursday at the Republican National Convention.

"We're special because dreams that are impossible anywhere else come true here," Rubio told thousands of convention delegates who were in turns rapt and raucous, listening to the son of a bartender and hotel worker who fled communist Cuba for America and what they hoped would be a better life for their children.

Rubio described how his bartender father stood in the back of packed banquet and convention halls serving drinks so that his son could one day stand at the podium in front of such a room.

"No one should be trapped in the circumstances of their birth," Rubio said as the crowd cheered and whistled its approval. "We should be free to go as far as our talents and work can take us."

"Because I was an American," Rubio said, "there was no limit to how far I could go."

But such potential can only be realized by future generations if Republicans succeed in replacing President Obama's "tired and old, big-government ideas [that] ... threaten to make America more like the rest of the world," Rubio said before introducing Romney to the convention that would formally nominate him as its presidential standard-bearer.

"The story of our time will be written by Americans who haven't even yet been born," Rubio said. "Let's make sure they write that we did our part. ... [That] we chose Mitt Romney to lead our nation and because we did, the 'American miracle' lived on for another generation to inherit."

Rubio, who has campaigned with Romney in Florida and Pennsylvania, quickly rose to stardom within the GOP after being elected to the Senate in 2010. His Cuban-American roots make him a valuable campaign surrogate for Romney, whose hard-line immigration policies have made it difficult for him to win support from Hispanics.

Obama has a nearly 40 percentage-point lead over Romney among Hispanics, recent polls show, and the Obama campaign was quick to assert that Romney's immigration policies would be hurtful to others trying to come to this country.

"Romney's immigration policy is nothing more than self-deportation," Obama's campaign said in a statement. "Despite the polished videos and speeches, Mitt Romney and Marco Rubio are just too extreme on immigration."