Having survived another of its perennial Perils of Pauline escapes, saved from extinction at the eleventh hour on Capitol Hill, the multibillion-dollar federal food stamp program now appears to be headed toward more severe budget problems.

Congress is well on its way to adopting President Reagan's proposed cuts for the program, which will mean that 1 million beneficiaries will drop from the rolls in fiscal 1982 and benefits will be reduced for more than 21 million others.

But congressional budget analysts calculate, and the administration agrees, that cuts of welfare, unemployment compensation and job-training will mean between $400 million and $600 million in new costs to the food stamp program next year -- costs that neither Congress nor the administration appears ready to underwrite.

Other estimates, including early data circulated informally by the Department of Agriculture before it officially submitted food stamp legislation, suggested that the nutrition program could be hit by at least an additional $1 billion in costs as fallout from the administration's overall austerity scheme.

In its official utterances on the subject, however, the administration has been far more guarded in projecting new obligations for the food stamp program, which, with its cost of $11.4 billion this year, is the largest federal welfare program.

Whatever the new costs, food stamp officials will be faced sometime next year with the prospect of cutting back benefits even further to help cover newly eligible recipients or having to ask Congress for more money.

G. William Hoagland, food stamp administrator at Agriculture, said this week that he intends to adhere strictly to congressionally imposed spending limits, even if they do not take the potential new costs into account.

"Once we decide how much we want to in that cap," Hoagland said. "If it means reducing benefits, that's what we will have to do."

Although Congress has locked a variety of food stamp eligibility changes into its budget reconciliation package, achieving savings of roughly $1.5 billion next year, the House and Senate still must agree upon caps -- spending limitations -- that the administration and its conservative allies want placed on the program. The Senate approved a food-stamp bill; the House has not yet acted.

"We hope we can build a cap that covers the spillover factors, the impact from other program cuts, and then have a full program," Hoagland said. "This a very important issue, very basic. The way we control government spending is to set a budget and then live by it. I intended fully to like within the ceiling."

The House Agriculture Committee and the Senate have adopted different caps in their respective food-stamp bills, but neither version as now written would come close to covering potential costs of the food stamp program in fiscal 1982 and succeeding years.

Senate and House moderates failed to win approval of "floating" caps that would move up or down, tied to the success or lack of success of the administration's economic recovery plan. The House committee, while adopting a tight limit on spending, warned that it would fall considerably short of the probable need.

What is involved here in part is a massive numbers game with no concrete numbers, based on economic assumptions doubted by many in Congress and caught squarely in the grip of big-league politics.

The last skirmishing over the program occurred last week on Capitol Hill, featuring an unusually bitter exchange between Sens. Jesse Helms (R-N.C.), the chief critic of food stamps, and Thomas F. Eagleton (D-Mo.).

The spat was precipitated by the administration's sudden recess-eve announcement that it would stop the program entirely on July 1 unless Congress gave the formal authorization for spending a supplemental appropriation of $1.7 billion to pay benefits through Sept. 30. Democrats on the Hill sensed a trap designed to run out the clock and blame them for shutting down the program.

The House quickly passed the authorization but Helms put a "hold on the measure in the Senate to prevent its quick passage. He amended it with fiscal 1982 benefits changes already adopted by the Argiculture Committee, of which he is chairman.

Helms called up the measure late on the night of June 25, as the Senate pressed toward adjournment, with just a handful of members present. Passage of his complicated package would have bounced the bill back to the House, which was preparing to leave on vacation the next day and thus would have been unable to resolve the issue before July 1. Without Senate passage of the House version, the administration would not spend the $1.7 billion.

Either eventuality would have struck a body blow to millions of food stamp recipients, automatically stopping payment of benefits for the final three months of the fiscal year. With only seven senators on the floor, at 1:15 the morning of June 26, Eagleton and Helms locked horns in a nasty confrontation.

Ignoring the administration's delay in making known its plans (the Carter administration last year gave five months' advance notice when money was running short), Helms blamed the House for putting the Senate in a last-minute bind.

Whatever, he added, "I believe we owe it to the taxpayers to take every precaution available to us to make sure that one of the most outrageously expensive and most abused programs in the history of the country will be brought under control.

"I do not begrudge helping any of the truly needy; but anybody who tries to pretend that this program does not need radical reform is just cockeyed."

Eagleton, in accusatory terms rarely heard on the floor, blamed Helms. "So let anyone who is a food stamp beneficiary know . . . that the man who did the program in -- insofar as having the benefits cut or terminated or having the notice go out on July 1 -- was the senator from North Carolina, the honorable Jesse Helms," he said. "There has been no more premeditated obstructionist of the food stamp program than the senator from North Carolina. He has fought it, maligned it, abused it, at every conceivable opportunity, at every hour of the day and night."

Grumbled Helms: "One day the people of this country are going to wise up to what is going on." But with Eagleton demanding a roll-call vote, Helms backed down and the simple House-passed version went through on a voice vote.