WASHINGTON (AP) — Alone in a cabin in Northern Ontario last month, Sen. Lamar Alexander considered the debt limit deal Congress and President Barack Obama had recently, noisily struck. He thought about the debates still to come in the 2012 election year, the issues he cared about, and his own future in the Senate.

Then the Tennessee Republican, 71, typed out a speech on his laptop and set it aside, to "let it cool."

Alexander served it up Tuesday, announcing from the Senate floor that he is giving up his No. 3 position in the GOP leadership for the freedom to write laws with Democrats, if need be.

"In the leadership, you always give up some of your independence in exchange for a seat at the table," Alexander said in a brief hallway interview. "I am giving up my seat at the table in exchange for some more independence."

It was an implicit rejection of the partisanship that has become the rule in a chamber designed to resolve the nation's toughest public policy questions.

But it wasn't clear, either, that Alexander would win an election to be the vote-counting whip under GOP leader Mitch McConnell, who set the tone early on by declaring the Republicans' top political priority would be denying Obama a second term in the White House.

Alexander listed other priorities in his speech Tuesday: reining in health care costs, curbing spending, creating jobs.

He spoke of his own freedom to help a deeply divided Senate function with rules that require 60 votes out of 100 to advance most major legislation.

"Stepping down from the Republican leadership will liberate me to spend more time trying to work for results on issues that I care the most about," he said. "I want to do more to make the Senate a more effective place to address serious issues."

Senate Republicans let Alexander go, praising his trustworthiness, his service, even his skill at the piano. Most of all, they congratulated him for not quitting the Senate altogether. Alexander said he would seek a third term in 2014.

"I am relieved," McConnell, a friend of 40 years, told the Senate. At a closed lunch later, Alexander's GOP colleagues gave him a standing ovation, several senators said.

Alexander's position as Republican conference chairman was never a comfortable fit. He was a protégé of former Sen. Howard Baker, R-Tenn., who was known in Washington as a "great conciliator," for his ability to forge consensus — a commodity rarely seen on Capitol Hill after the tea party-fueled Republican resurgence in last year's elections.

"He accepted his role, and he did it well," Baker said in a telephone interview Tuesday.

Alexander was careful to invoke his conservative credentials. He described himself as a "very Republican Republican" and rejected the notion that Congress is overly divisive. Vice President Aaron Burr killed Treasury Secretary Alexander Hamilton in an 1804 duel, Alexander pointed out. And Rep. Sam Houston caned an Ohio lawmaker. Then, Alexander said, there were venomous debates during the Civil War, the Army-McCarthy hearings, Watergate and Vietnam.

"To suggest that we should be more timid in debating the issues is to ignore American history and the purpose of the Senate," Alexander said.

With the retirement of the GOP whip, Sen. Jon Kyl, R-Ariz., Alexander faced the opportunity to try to step up and fill the No. 2 job — and a potentially divisive race against Senate GOP campaign chairman John Cornyn of Texas. In 2006 Alexander lost a bid for the whip's job to then-Sen. Trent Lott, R-Miss., and Senate Republicans have become more conservative since then.

Alexander's demurral should ease Cornyn into the whip's post. Sen. John Thune, R-S.D., said he will run to succeed Alexander as chairman of the Republican Conference.