By LAURIE KELLMAN

WASHINGTON — How does a musician-senator fill the time during yet another partisan Senate stalemate?

In Sen. Lamar Alexander’s case, he sits down at a borrowed piano in his Capitol Hill office and, with a grin, bangs out “The Memphis Blues.”

He’s been blending music and politics his whole life. And this coming week, the three-term Tennessee Republican hopes Democrats and the GOP harmonize as the Senate becomes Alexander’s stage.

The son of a schoolteacher and principal, this former federal education secretary and onetime university president will be shepherding a bill he’s been working on for seven years: a rewrite of the contentious No Child Left Behind law.

Alexander acknowledges “getting a little emotional” when his polarized committee – the Senate Health, Education, Labor and Pensions Committee – approved the measure unanimously this spring. “But,” he said in an interview, “I’m going to save my emotions until we get a presidential signature.”

The carefully balanced legislation is a long way from becoming law and faces an uncertain future in the House. But it’s perhaps the most consequential shot Alexander will have at a lifelong effort to loosen the federal government’s grip on public schools.

“Legacy, to him is not, ‘I need to do something so people will remember my name,’” said Democrat Phil Bredesen, who, like Alexander, is a former Tennessee governor who made education a priority. “For him, it’s that, ‘I need to leave a mark that will do good things in the future.’”

For the 75-year-old Alexander, the bill’s success would punctuate a legislative career fueled by pragmatism and the drive for results, a sharp contrast to new GOP colleagues such as Sens. Ted Cruz of Texas and Rand Paul of Kentucky, who have blocked legislation and are proud of it.

Senate Majority Leader Mitch McConnell, R-Ky., holds up the product of Alexander’s negotiations with his Democratic co-sponsor, Sen. Patty Murray of Washington state, as a model for the way he wants the Senate to work under GOP control.

“I think the way he navigated a committee that has the most liberal members of the Senate and a few of the most conservative, to get to this point, is why I was willing to give this issue floor time,” the schedule-setting McConnell said in a recent interview. “In my job, floor time is the coin of the realm. It means that I have confidence that the underlying bill is going to succeed.”

The proposed rewrite stands on the premise that states and localities are better positioned to assess their own school performance than what Alexander calls the “national school board” created by the 2001 law that Republican President George W. Bush championed.

It helped that Republicans and Democrats – and the army of teacher and education lobbyists swarming around the rewrite – agree on that general idea, Alexander says. The turning point came earlier this year as Republicans assumed control of the Senate, when Murray suggested that she wanted to get an agreement.

“He comes to the negotiating table with a very strong philosophy, and what he thinks is right, but he also understands the art of compromise,” Murray says.

For the first time, the proposal will get a debate and likely vote on the Senate floor.

“It’s a chance for him to leverage all of those experiences that he had as governor, as secretary of education and president of the University of Tennessee,” said Sen. Bob Corker, R-Tenn.

For all of the platforms from which Alexander has advocated for education, the bully pulpit of the presidency was not to be among them. He lost the 1996 GOP nomination to Kansas Republican Bob Dole despite a splashy campaign featuring Alexander’s red-and-black plaid flannel shirt. Four years later, Alexander tried again, but Bush won the party nod. In 2002, Alexander ran for and won the Senate seat vacated by retiring GOP Sen. Fred Thompson.

Being a Senate pragmatist in the subsequent polarizing years drew derision from the GOP’s increasingly powerful conservatives, who helped Republicans claim the House majority in 2010. After the bitter budget and debt ceiling deal in summer 2011, Alexander retreated to a cabin in northern Ontario. He returned to Washington and stepped down from his No. 3 post in the party’s leadership, an implicit rejection of the partisan warfare that had so energized the GOP but brought the nation to the brink of default.

Conservatives noticed, calling him “liberal Lamar” and a “mushy moderate,” but Alexander defeated primary challenger Joe Carr and won re-election last year.

These days, the red-and-black flannel shirt is mounted prominently in Alexander’s Capitol Hill office, near a 27-foot barn wall festooned with antiques on loan from a Tennessee museum. Around the corner is the piano on which Alexander sometimes noodles, sending music floating down the stark government hallway.

The piano plays a prominent role in Alexander’s public life.