WASHINGTON (Reuters) - The U.S. Congress early on Saturday passed a measure to boost Social Security retirement payments to some retirees who draw public pensions - such as former police and firefighters - which critics warned will further weaken the program's finances.

The Senate in a 76-20 bipartisan vote shortly after midnight approved the Social Security Fairness Act, which would repeal two-decades-old provisions that can reduce benefits for people who also receive a pension.

The House of Representatives last month approved the bill in a 327-75 vote, which means that Senate approval sends it to Democratic President Joe Biden to sign into law. The White House did not immediately respond to a question about whether Biden intended to do so.

The bill will overturn a decades-old change to the program that had been made to limit federal benefits to some higher-earning workers with pensions. Over time, growing numbers of municipal employees such as firefighters and postal workers also saw their payments capped.

Most Americans do not participate in pension plans, which pay a defined benefit, and instead are dependent on what money they can save and Social Security. Just one in ten U.S. private sector workers have pension plans, according to Labor Department data.

The new provisions impact about 3% of Social Security beneficiaries - totaling a little more than 2.5 million Americans - and the workers and retirees affected by these provisions are key constituencies for lawmakers and their powerful advocacy groups have pushed for a legislative fix. 

Some of them could received hundreds of dollars more a month in federal benefits as a result of the bill, retirement experts said.

Some federal budget experts warned the change could hurt the program's already shaky finances as the bill's price tag is approximately $196 billion over the next decade, according to an analysis by the non-partisan Congressional Budget Office.

Emerson Sprick, associate director of economic policy at the Bipartisan Policy Center, said in an interview, "the fact that there is such overwhelming support in Congress for exactly the opposite of what policy researchers agree on is pretty frustrating." 

Instead of scrapping the current formulas for determining retirement benefits for these workers, revisions have been floated, as well as more accurate communication from the Social Security Administration on how much money these public sector employees should expect. 

The Committee for a Responsible Federal Budget, a nonpartisan fiscal think tank, is also warning the extra cost will affect the program's future. 

"We are racing to our own fiscal demise," the group's president, Maya MacGuineas, said in a statement.

"It is truly astonishing that at a time when we are just nine years away from the trust fund for the nation's largest program being completely exhausted, lawmakers are about to consider speeding that up by six months."

Republican Senator Ted Cruz on the Senate floor on Wednesday said the bill as written will "throw granny over the cliff".

"Every senator who votes to impose $200 billion dollars of cost on the Social Security Trust Fund, you are choosing to sacrifice the interest of seniors who paid into Social Security and who earned those benefits," he said.

Bill supporters said Social Security's future can be addressed at a later time. 

Asked about the solvency implications pf this legislation, Senator Michael Bennet, a supporter of the bill, told Reuters: "Those are much longer term issues that we have to find a way to address together."

(Editing by Stephen Coates)