LeMieux — who was appointed to fill the last 16 months of Sen. Mel Martinez's term — said he couldn't compete against the Fort Myers' congressman's famous name and fact the establishment had already gotten behind Mack.
LeMieux said he didn't have the money for widespread television ads to counter Mack's name recognition. Mack's refusal to debate, LeMieux went on to say, would not allow voters statewide to compare the two candidates.
He also said his decision will give the party a better chance of beating Democratic Sen. Bill Nelson come November.
"To continue would only hurt our chances in the fall, and that is not something I will risk," the former senator said in video message emailed to reporters and supporters. "Connie Mack will be our nominee. He has my support."
The decision, experts said, essentially locks up the nomination for Mack.
"George LeMieux was his most serious opponent," said Peter Bergerson, a political science at Florida Gulf Coast University.
"With him out of the picture, the other candidates are virtually unknown statewide. They lack the resources, money and name recognition."
Mack has been considered a frontrunner since throwing his hat in the race last year. A recent Quinnipiac University poll showed Mack ahead of LeMieux by more than 30 percentage points.
Mack is helped by the name he shares with his father, a former senator, and his great-grandfather, the Hall of Fame baseball manager.
"It would take a political tsunami to defeat Connie Mack in the primary now," said Bergerson.
But despite the fact Mack may be leading in the polls, the remaining candidates said they have no plans to back down in the waning days of the campaign.
"We're going to continue to do what we're doing," said retired Army Col. Mike McCalister. "We're doing some good."
McCalister is among a handful of little known Republicans seeking the nomination. Former U.S. Rep. Dave Weldon, who entered the race just before the qualifying deadline, Deon Long and Ave Maria resident Marielena Stuart are also running.
Weldon said LeMieux's decision to drop out will be good for him in the long run.
"George was not gaining traction and he's been in the race for 16 months," Weldon said. "People are contacting me pretty rapidly. There's people who supported George LeMieux who are not going to support Connie Mack."
Stuart, like the remaining candidates, is hopeful LeMieux's supporters will become hers.
"It is critical that Republicans unite behind the powerful and positive solutions that Marielena Stuart will deliver on the floor of the U.S. Senate on behalf of all Floridians," Stuart's campaign said in a statement.
Long could not be reached for comment Wednesday.
The remaining candidates may be hopeful, but Mack has already been campaigning as though he is the nominee. He refused to debate his primary opponents, and has emailed supporters and potential donors he wants to take the fight directly to Nelson.
"I urge all the citizens of Florida who want less government, less taxing less spending and more freedom to now join with us in our campaign to defeat Bill Nelson and to help Mitt Romney to defeat Barack Obama," Mack said in a statement.
"This election is the most important in our lifetime. Together we will in November and restore America's promise and purpose."
This article contains material from the Associated Press.