An end-of-the-year scramble to curb the federal budget deficit might seem like an inauspicious time for a congressman to secure hundreds of millions of dollars in increased funding for a Great Society program. That is, unless the lawmaker is Rep. Henry A. Waxman (D-Calif.).

As his colleagues raced to complete budget-cutting and tax-raising bills in time to adjourn for Christmas, Waxman was fighting to preserve provisions that would enlarge Medicaid, the federal health program for the poor. His efforts provoked outraged opposition from the Reagan administration. "Right in the middle of budget reduction," exclaimed one White House official, "this guy is pushing one of the biggest expansions ever of a social welfare program!"

In the end, Waxman settled for provisions that would add an estimated $600 million to Medicaid over three years. That was about one-fourth of what he had sought. But a quarter of a loaf is considerably more than most other members of Congress can obtain for their favorite programs these days.

"We didn't get all of what we wanted," Waxman said. "We didn't lose it all, either." One result is that Medicaid will start covering thousands of low-income pregnant women and infants who do not now qualify for benefits because their family incomes exceed the poverty line. Another result is that nursing homes serving Medicaid patients will be required to meet considerably tougher standards.

In an age of fiscal frugality, Waxman is an unabashed advocate of spending more to provide better health services to the disadvantaged. Each year since 1983 he has used his position as chairman of the House subcommittee on health and the environment to expand health programs for the poor and elderly, either by increasing benefits or creating new ones. The slow, incremental pace at which he is forced to operate illustrates the difficulties that Democrats face in advancing a liberal agenda. But Waxman's record shows that with patience, persistence and skill, a liberal lawmaker can make headway within the confines of Reaganomics.

"Waxman is just a brilliant, tough legislator," said Deborah Steelman, a Washington lawyer who battled him in her previous job as associate director of the president's Office of Management and Budget. "At the beginning of every year, he'll ask for the sky. And when he gets only the moon instead of the whole sky, he still ends up getting more than most legislators get in 10 years."

This year, Waxman faced unusually formidable obstacles. His colleagues were professing a new sense of determination to curb the deficit in the wake of the Oct. 19 stock market plunge, and leaders of both parties were strongly backing the accord they struck with President Reagan to save $76 billion over the next two years. So, even though Waxman had persuaded the House and Senate to pass some of his proposals in previous years, he knew he would be unable to salvage them all in the final budget compromise.

The Reagan administration, meanwhile, was redoubling its efforts to thwart him. An internal administration document targeted Waxman as "particularly expert" at budgetary games such as "delayed-action fuses," by which programs are expanded in ways that cost relatively little in the first couple of years but add billions to outlays three or four years in the future. In a letter to lawmakers, OMB asserted that Waxman's Medicaid proposals would cost $3.8 billion by 1992.

Waxman and his allies disputed OMB's figures, citing lower estimates of the programs' costs compiled by the Congressional Budget Office. But even the CBO figures showed that Waxman's proposals would add more than $1 billion to spending by 1990. "This is no way to solve the long-term structural deficit problem," complained Carol Cox, president of the Committee for a Responsible Federal Budget, a group of prominent citizens and former government officials.

Countered Robert Greenstein, executive director of the Center on Budget and Policy Priorities, a liberal research group: "What Henry Waxman is trying to do on Medicaid is mend one of the egregious holes in the safety net in the United States. There's virtually no other industrialized country in which you would have low-income pregnant women and young children with no health-care coverage whatsoever."

Late last week, Waxman was digging in his heels as House-Senate conferees wrangled over details of the budget package. "To Henry, 'negotiating' means that you give in while he sticks by his position," Sen. John H. Chafee (R-R.I.) said.

But at a Sunday afternoon meeting in the Capitol with top Democratic leaders, Waxman finally began to bargain away some of his most cherished proposals. Sen. Lloyd Bentsen (D-Tex.), chairman of the Finance Committee, told the group that OMB had made a convincing threat that the president would veto the package if it included certain Waxman-sponsored provisions. One would provide temporary Medicaid benefits to poor people who get off the welfare rolls by finding jobs. Another would allow the spouse of a Medicaid patient in a nursing home to keep considerably more income and wealth than is currently permitted.

Waxman agreed to drop both items. But he stands a good chance of getting them enacted in other pending legislation, including a welfare-revision bill and a bill providing insurance against catastrophic illness.

Grumbled a senior administration official, "He'll live to fight another day."