By Deborah Charles

TAMPA, Florida (Reuters) - U.S. Senator Marco Rubio made his first major speech at the Republican National Convention on Thursday, and his eloquence and ease on stage suggested it won't be his last.

The first-term senator from Florida had the daunting task of introducing Mitt Romney as the party's nominee to challenge Democratic President Barack Obama in the November 6 election.

Coming on stage after movie star Clint Eastwood gave a rambling and at times incoherent speech, Rubio took the pressure in stride and quickly had the sign-waving crowd eating out of his hands.

The 41-year-old told how his parents came to the United States from Cuba in search of a better life and worked long hours to make sure Rubio and his siblings could succeed.

"My dad was a bartender. My mom was a cashier, a hotel maid and a stock clerk at K-Mart," he said. "They never made it big. They were never rich.

"And yet they were successful," he said. "Because just a few decades removed from hopelessness, they made possible for us all the things that had been impossible for them."

Rubio, a favorite of the conservative Tea Party movement who had been rumored to be a possible vice-presidential pick for Romney, was the last in a series of young conservatives to take the stage this week at the Republican convention.

"He's a bright and shining star in the Republican party, there's no question about that," said Bill Bunting, a delegate from Florida. "We're just blessed with all the young people who are coming into politics."

Speaking at their party's national convention can often help politicians solidify their position. In 2004, Obama - then a state senator running for a U.S. senate seat - delivered an electrifying speech at the Democratic National Convention that helped catapult him onto the national political scene.

Rubio had the crowd roaring and cheering as he criticized Obama for dividing the country and for failing to live up to his past promises of hope and change.

"In the end, in this election, it doesn't matter how you feel about President Obama. This election is about your future, not his.

"This election is not simply a choice between a Democrat and a Republican," Rubio said. "It's a choice about what kind of country we want America to be."

Rubio could be a vital link for Romney to the key Latino community. Obama leads Romney among Hispanic voters by about 40 percentage points, putting pressure on Republicans to become more competitive in states where the Latino vote could be decisive in November, such as New Mexico and Nevada.

Kim Bacchus, a delegate from Reno, Nevada, said Rubio's story as a first-generation-born American is one of his strengths.

"I think Marco Rubio represents all that is good about America," she said. "He's the best spokesperson for the American dream." (Additional reporting by Andy Sullivan; Editing by Leslie Adler)