WASHINGTON — Come January, nearly 60 million Social Security recipients will get benefit increases averaging $20 a month, the third straight year of historically small pay hikes.

The 1.7 percent cost-of-living adjustment, or COLA, will also boost government benefits for millions of disabled veterans, federal retirees and people drawing disability payments for the poor.

Year after year of tiny increases are weighing on many older Americans.

“What is it going to cover? Not even the cost of one medicine,” said Louis Grosso, a 66-year-old retired doctor who lives in Philadelphia. “Do you know how much my cholesterol medicine is?”

The government announced the benefit increase Wednesday when it released the latest measure of consumer prices. By law, the increase is based on inflation, which has been below historical averages so far this year.

For example, gasoline prices have dropped over the past year while the cost of clothing is up by less than 1 percent, according to the September inflation report.

Even medical costs, which disproportionately affect older Americans, are up just 1.9 percent over the past year.

Meanwhile, the amount of Americans’ wages subject to Social Security taxes is also going up.

Social Security is financed by a 12.4 percent payroll tax on the first $117,000 of a worker’s wages — half is paid by the worker and half is paid by the employer. Next year, the wage cap will increase to $118,500, the Social Security Administration said.

As for payments to beneficiaries, Congress enacted automatic increases in 1975, when inflation was high and there was a lot of pressure to regularly raise benefits.

For the first 35 years, the COLA was less than 2 percent only three times. Next year, the COLA will be less than 2 percent for the third straight year, and the fifth time in six years.

This year’s increase was 1.5 percent, the year before it was 1.7 percent.

“While any increase is better than no increase, the fact of the matter is that for millions of seniors, retirees and federal employees, these annual increases will be gone before most even receive them,” said J. David Cox, national president of the American Federation of Government Employees.

In all, the COLA affects payments to more than 70 million Americans — more than a fifth of the country.

About 59 million retirees, disabled workers, spouses and children get Social Security benefits. The average monthly payment is $1,192.

The COLA also affects benefits for about 4 million disabled veterans, 2.5 million federal retirees and their survivors, and more than 8 million people who get Supplemental Security Income, the disability program for the poor. Many people who get SSI also receive Social Security.

By law, the cost-of-living adjustment is based on the Consumer Price Index for Urban Wage Earners and Clerical Workers, or CPI-W, a broad measure of consumer prices generated by the Bureau of Labor Statistics. It measures price changes for food, housing, clothing, transportation, energy, medical care, recreation and education.

The COLA is calculated by comparing consumer prices in July, August and September each year with prices in the same three months from the previous year.

“In the last several years we have had extremely low inflation,” said economist Polina Vlasenko, a research fellow at the American Institute for Economic Research. “Basically because inflation is low, the cost-of-living adjustment is going to be low, too. It’s supposed to just compensate you for inflation.”

President Barack Obama and some Republicans in Congress have expressed support for a more conservative measure of inflation that would, on average, result in smaller COLAs. Obama included the new “chained CPI” in his 2014 budget proposal, but he left it out of his proposal for 2015.

For next year, the chained CPI would have resulted in a benefit increase of 1.6 percent.

Many Democrats in Congress and advocates for older Americans have panned the chained CPI. They want a more generous COLA that, they say, would better reflect price increases faced by older Americans who tend to spend more of their income on health care.

The rise in medical costs has slowed in recent years, but people hit with serious illnesses can still see their individual costs soar.

“Seniors across this nation understand how important having an accurate measure of their real costs is to their day-to-day survival,” said Max Richtman, who heads the National Committee to Protect Social Security and Medicare. “While there has been a lot of talk in Washington about the need to find a more accurate COLA formula, unfortunately that attention has largely focused on ways to cut the COLA even further.”

The White House has said Obama would accept the new inflation measure only as part of a larger deficit reduction package that also included tax increases. Such a “grand bargain” has been elusive in Obama’s first six years in office.