WASHINGTON — An unusual alliance of tea party enthusiasts and liberal leaders in Congress is pursuing major changes in the country’s mandatory sentencing laws.

What’s motivating them are growing concerns about both the fairness of the sentences and the expense of running federal prisons.

The congressional push comes as President Barack Obama and his Cabinet draw attention to the issue of mandatory sentences, particularly for nonviolent drug offenders.

Supporters say mandatory minimum sentences are outdated, lump all offenders into one category and rob judges of the ability to use their own discretion.

They also cite the high costs of the policies. The Justice Department spends some $6.4 billion, about one-quarter of its budget, on prisons each year, and that number is growing steadily.

“People are coming here for different reasons, but there is a real opportunity,” said Sen. Dick Durbin, D-Ill., one of the Senate’s leading proponents of sentencing changes.

The push is being led by the Senate, where Durbin has worked with tea party stalwarts such as Sen. Mike Lee, R-Utah, on legislation that would give judges more flexibility to determine prison sentences in many drug cases. At the same time, a right-left coalition is pressing for changes in the House.

Prison costs have soared in the past 30 years, when laws requiring mandatory prison time for many drug offenses were put in place.

The yearly cost for one federal inmate ranges from $21,000 to $33,000 depending on the prison’s level of security. About half of the nation’s more than 218,000 federal inmates are serving time for drug crimes — and virtually all of them faced some form of mandatory minimum sentencing.

Tough-on-crime drug policies once united Republicans and Democrats who didn’t want to appear weak on crime. Now reversing or revising many of those policies is having the same effect.

The Fair Sentencing Act, passed in 2010, drew bipartisan support for cutting penalties on crack cocaine offenses. The bill reduced a disparity between crack-related sentences and sentences for other drugs, though it only addressed new cases, not old ones.

Durbin, one of that bill’s chief sponsors, has written a much broader bill with Lee, called the Smarter Sentencing Act. It would expand a provision that gives judges discretion for a limited number of nonviolent drug offenders. The new law would allow judges the same latitude for a larger group of drug offenders facing mandatory sentences.

It’s one of four bills dealing with sentencing that the Senate Judiciary Committee is expected to take up early in the year. The committee chairman, Sen. Patrick Leahy, D-Vt., said he wants one consensus bill to clear the committee.

Leahy is a co-sponsor on the Durbin-Lee bill but has also introduced legislation with Sen. Rand Paul, R-Ky., that would expand the safety valve even more, to all federal cases with mandatory sentences if certain conditions are met.

Sen. John Cornyn, R-Texas, introduced legislation late in December that is based on changes in Texas’ state prison system.

A separate bill, sponsored by Sen. Sheldon Whitehouse, D-R.I., and Sen. Rob Portman, R-Ohio, allows inmates to earn credit for completing programs designed to reduce recidivism.

Leahy’s committee delayed writing a sentencing bill several times in 2013. But supporters noted that the last sentencing legislation took months to negotiate and said that the committee has delayed work until early 2014 in large part because behind-the-scenes talks are proving fruitful. Durbin said he and Lee had been lobbying their fellow committee members — Durbin talking to skeptical Democrats, Lee to Republicans.

In the House, Rep. Raul Labrador, R-Idaho, a tea party conservative, and Rep. Bobby Scott, D-Va., are co-sponsors of a companion to Durbin and Lee’s bill.

A number of outside groups have expressed support for the Durbin-Lee bill, too, and they run the ideological spectrum, including the conservative Heritage Action, the American Bar Association, the NAACP and the American Civil Liberties Union.

In August, Attorney General Eric Holder called on Congress to make permanent changes in sentencing laws and instructed federal prosecutors to stop charging nonviolent drug offenders with crimes that carry mandatory minimum sentences.

Just before Christmas, Obama used his presidential powers to press the issue. He commuted the sentences of eight people serving long drug sentences.