WASHINGTON — Unemployed workers would no longer be able to claim 99 weeks of benefit checks by this summer under a deal being worked out in Congress.

Under this week’s compromise for extending a Social Security tax cut through the rest of 2012, federal unemployment benefits for people who have been out of work more than six months are being scaled back.

If Congress passes the bill and President Barack Obama signs it into law, the current maximum 99 weeks of benefits will gradually fall to 73 weeks by September. For people in all but about a dozen of the highest unemployment states, the benefits will be cut off after 63 weeks.

Democrats had hoped to keep the number as close as possible to 99 weeks, arguing that the benefits are critical for those struggling to make ends meet and provide a boost to the economy. Republicans wanted to reduce the maximum time span for benefits to 59 weeks, saying too many people don’t seriously look for a job until the government checks quit coming.

The agreement would let both parties claim victory: Democrats can say they preserved the program for another year, while Republicans may claim they won major concessions by scaling back the program.

About 43 percent of the nation’s nearly 13 million unemployed have been without work for more than six months, double the rate of any other economic downturn since the Great Depression. If Congress had not reached a deal to reauthorize the program, about a million people would have lost benefits next month.

“It’s far from perfect, but it seems to be a responsible approach to the current problem of long-term unemployment,” said George Wentworth, an attorney with the National Employment Law Project, a worker advocacy group that supports long-term benefits.

It was not immediately clear how many people might lose out on benefits later this year under the new plan. Currently, 22 states are eligible for 93-plus weeks of unemployment insurance; just 18 get the full maximum of 99 weeks. The average unemployed worker receives less than $300 a week in benefits.

Wentworth said the gradual decrease would help cushion the blow for those relying on the benefits.

The plan would extend the current 99-week maximum through May for states with the highest unemployment rates. Benefits would drop to 79 weeks in June and to 73 weeks in September. Unless Congress extends the federal benefits again, people losing their jobs after July 1 will get only 26 weeks.

“This agreement is a step in the right direction,” said James Sherk, a policy analyst at the conservative Heritage Foundation. “However, two years of benefits was excessive when passed, and a year-and-a-half of benefits in an improving labor market is still excessive.”

The program was already starting to wind down anyway. Under the current formula, the maximum coverage period would have fallen to 79 weeks in October.

The job market has been steadily improving, and fewer people are filing for the benefits. On Thursday, the Labor Department reported that the number of people seeking unemployment benefits last week was the lowest it’s been in four years.

But Heidi Shierholz, a labor economist with the liberal Economic Policy Institute, said it’s still too soon to cut back on benefits.

“Even if we continue growing at the current rate, given the depths of the job deficit that we’re in, we’re not going to be at a place by May where job opportunities are plentiful,” she said. “Layoffs are back to pre-recession levels, but hiring is still extremely slow.”

The new law will allow states to make benefit applicants take drug tests if they lost their job because they failed a drug test or are applying for a job that requires one. Republicans dropped an effort to let states require all applicants to take a drug test, or require applicants without a high school diplomas to pursue a GED certificate.