The family budgets of 170,000 Washington area persons could be pinched severely at the beginning of next month if Congress fails to meet a deadline next week for providing funds for the federal food stamp program.

While it appears that Congress will approve the funds needed to keep the program going, it is touch-and-go whether it will pass the necessary legislation by May 5. If the deadline is not met, Agriculture Secretary Bob Bergland must order all states to suspend food stamp benefits, effective June 1.

"It really scares me," said Mary E. Williams, 52, of Northwest Washington, who receives $33 worth of food stamps a month in addition to $243 from other assistance programs. "If I don't get my food stamps next month, I don't know what I'll do. I have to buy food. I guess some of my other bills will have to go."

"I'm telling you the truth, it's going to be really rough for me and lots more people."

Jane Mattern, a public information officer with Agriculture's Food and Nutrition Service, said yesterday it is "extremely unlikely" that the deadline will be met. "Congress intends to provide the money, but now it doesn't look like it will be in time to prevent a delay in June benefits."

Congressional staff members said, however, that they thought Congress would make the deadline -- meeting into the late hours of the night if necessary.

The Agriculture Department spokeswoman said that if it looks like Congress will just miss the deadline, Bergland can tell the states to be prepared to start up their food stamp operations again quickly. She said that the time needed to gear up again would vary from state to state.

Under the program, 21.4 million people nationwide get food stamps, which they can use like money to buy food at grocery stores. A family of four that earns no income, for example, qualifies for $209 a month in stamps.

In the District, where 103,000 people get $3.4 million worth of food stamps each month, United Planning Organization staff member Linda Greenan is worried. "People are incredibly dependent on food stamps," she said. "If they're late, people panic."

Greenan said local agencies will meet today with church groups and community workers to set up an emergency food network to coordinate activities such as canned food drives But she said such emergency measures probably would be inadequate.

"It's never been like this. Even the president is lobbying," Greenan said. "It scares the hell out of me."

On Monday, President Carter told a national conference of the League of Women Voters in Washington that the prospects for averting the cutoff "are not good."

Carter said the cutoff "will create a horrendous problem in our country, not only the disillusionment of those who might be hungry, but enormous lines of people outside welfare offices throughout the country searching for some alternative."

By law, he noted, "the bureaucratic structure" will have to shut down. "It will take a while to get it back into motion when the Congress finally acts."

In 1977, Congress imposed a $6.2 billion ceiling for this fiscal year on the food stamp program. But higher unemployment, rising food costs and increased participation in the program have sharply boosted its cost. Agriculture Department officials estimate that $8.3 billion in benefits will be needed for this fiscal year, which ends Sept. 30.

In Fairfax County alone, for example, the number of food stamp recipients increased from 5,088 to December 1978 to 10,588 in March of this year, according to Edward Admundison, assistant director of the county's social services department.

Many persons still will receive other welfare and Social Security benefits, Admunson noted, "It a food stap cutoff) will not mean that they are completely in the cold. But it may be a choice of buying food or paying their rent.. This is not a poverty-ridden area, but it will be a terribly anxious time for some residents."

In the District, Muriel Yaeger, food stamp outreach coordinator for the Department of Human Services, said she, too, is concerned. "We don't want to alarm the public dramatically. We're cautioning recipients to use their May food stamps wisely because there is a possibility it may have to last two months."

James A. Buford, head of the department, yesterday asked community groups, churches, D.C. public schools and national grocery chains in the area to help provide food for families who may need assistance.

For the food stamp program to continue without interruption, Congress must do three things. It must complete action on a revised budget for fiscal 1980. It must approve legislation authorizing the food stamp program, which will include the funds as well as making changes in the program. And it must approve legislation to appropriate funds for the program. The legislation is at varying points along a complicated path of congressional committees of the House and Senate and final votes in the full chambers.

"I think we'll make it on the edge of the cliff," said Joseph Crapa, a staff member of the House Agriculture subcommittee on Nutrition. "We realized there might be a crisis two months ago."