Updated

LEXINGTON, Ky. -- Front-runner Rand Paul said in a U.S. Senate debate Monday night that he may not support Kentucky's other senator, Mitch McConnell, for minority floor leader if he's elected.

"I'd have to know who the opponent is and make a decision at that time," Paul said in a sometimes testy televised debate, the final face off in what has become an increasing acrimonious race to replace Sen. Jim Bunning.

His chief Republican opponent, Kentucky Secretary of State Trey Grayson, said he "would proudly cast a vote for Sen. McConnell." McConnell endorsed Grayson in the May 18 primary. South Carolina Sen. Jim DeMint, who endorsed Paul, has been mentioned as a potential McConnell opponent for minority leader, though DeMint has said he has no such intention.

Paul is considered an outsider to the Republican political establishment, which has supported Grayson. Paul, a Bowling Green eye surgeon, is leading in the polls.

Paul has strong backing from tea party activists, who have been increasingly showing their political power this year. They most recently helped topple three-term Republican Sen. Robert F. Bennett of Utah at that state's GOP convention over the weekend.

Paul took a hard line against congressional earmarks during the debate, saying he is philosophically opposed to pork barrel projects that have been used to pay for programs across Kentucky unless Congress has the money in hand to pay for them. Grayson said some of the earmarks, like those used to fight drug trafficking, are vitally needed and he would support them.

The eventual Republican nominee will face one of five Democratic candidates, including Lt. Gov. Daniel Mongiardo and Attorney General Jack Conway.

Paul and Grayson are the only two Republicans who have enough money to run competitive campaigns. Each candidate had raised about $2.4 million as of mid-April, with most of the money being spent on TV advertising. Both sides have been airing attack ads in recent weeks.

Grayson ads have accused Paul of being unfriendly to the coal industry, a key segment of the Kentucky economy employing some 17,000 people, and of being soft on abortion, an important issue among the state's evangelical voters. Paul ads have accused Grayson of being part of the Washington establishment and have tried to connect Grayson, a former Democrat, to President Barack Obama.

In the Monday night debate, Grayson took Paul to task on national security issues, accusing him of wanting to release suspected terrorists held at Guantanamo Bay and saying he isn't concerned that Iran may be trying to development nuclear weapons. Paul retorted that Grayson has taken previous comments out of context, and accused him of being "intellectually dishonest" by making the claims.

Grayson also challenged Paul's credentials as an abortion opponent, saying he had changed his stand after entering the Senate race to win the support of Kentucky evangelicals. Paul said he has always opposed abortion, first taking a stand against it as a teenager and later as a medical student refusing to perform such procedures.

Paul called Grayson's assertions that he isn't opposed to abortion "gutter trash," and chided him saying "You know it's a lie."

Kentucky's two sitting Senators are on opposite sides in the race, with Bunning giving Paul his endorsement.

Bunning, who was considered politically vulnerable to potential Democratic challengers, dropped his re-election bid because he had been unable to raise enough money to mount a formidable campaign. Bunning blamed McConnell and other Republican leaders for drying up his fundraising, so when the Republican establishment got behind Grayson, a chafed Bunning threw his support to Paul, calling him "a man of integrity" and "the only true conservative" in the race.

Paul is the son of Texas congressman Ron Paul, who made an unsuccessful bid for the GOP presidential nomination in 2008. The younger Paul has capitalized on his father's political base for fundraising.

Besides McConnell, Grayson has won endorsements from former Vice President Dick Cheney and former New York City Mayor Rudy Giuliani. He also has the endorsement of U.S. Rep. Hal Rogers, a revered political figure in heavily Republican southeastern Kentucky.

Paul has endorsements from former Alaska Gov. Sarah Palin, former GOP presidential candidate Steve Forbes and evangelical leader James Dobson.