House Democrats said yesterday Congress would wake up the morning after and find it had swallowed all sorts of "sleepers" along with the Reag an budget-cut bill, which was the thickness of a telephone book and which most members had not read when they voted.

One such provision, they said, would let Office of Management and Budget Director David A. Stockman redefine poverty in America.

The official poverty line is the basis for admission into many federal benefit programs. Those below get in, those above do not, or not as frequently. He who defines the line controls the programs, to a large degree.

In the past the poverty threshold, which is about $8,400 for a family of four, less for a smaller household, more for a larger, has been raised automatically each year with inflation.

About 11.6 percent of the population is below the threshold. But some conservatives say this figure is deceptive, in that it takes no account of non-cash or in-kind income -- Medicaid benefits, for example, or food stamps or rent supplements.

Majoritry Leader James C. Wright Jr. (D-Tex.) told the House that the poverty-line provision would put "power in the hands of one man . . . virtually to demolish all the array of programs established by the Congress." He said it could endy by allowing Stockman unilaterally to strip people from the welfare rolls -- at which point the Republicans applauded.

Later, however, Edwin Dale, spokesman for Stockman, dismissed the Wright charge as plain wrong, on grounds that OMB already has final responsibility for the official poverty definition and has had it for almost a decade; he said the Republican language merely restates this because the old language is being repealed elsewhere in the budget reconciliation package.

The Reagan alternative, as drafted for the floor, contained several other provisions that some Democrats cited as "sleepers."

For example, Republicans on the House Education and Labor Committee succeeded in completely rewriting as part of the bill the Federal Employes Compensation Act that governs workmen's compensation for federal employees injured while working.

By a variety of methods, it reduces benefits to save the government an estimated $76 million in fiscal 1982 and about $800 million over fiscal years 1982 to 1986. The provision wouldn't merely cut total amounts, but would change benefit levels, require a longer waiting period, eliminate a 45-day grace period in which a person filing a claim can get full pay, and require a beneficiary to shift to retirement rolls, often with lower benefits, at 65.

The dispute about who defines the poverty line was a flashpoint because some leading figures in the administration, like White House aide Martin Anderson in a book written before the Reagan administration came to power, as well as Department of Health and Human Services Secretary Richard S. Schweiker in his welfare proposals, have indicated they want to look at need in a different way.

At present the poverty index, which was developed by Mollie Orshansky at the Social Security Administration in the 1960s, counts only cash income in determining poverty.

Anderson or others have said that non-cash income, such as food stamps, the imputed value of Medicare and Medicaid benefits, housing subsidies and other in-kind income also should be counted. The Congressional Budget Office has calculated that if that were done, the percentage of people in poverty would be only about 6.2 percent of the general population instead of the Census Bureau's recent 11.6 percent calculation. This would then justify withholding added aid to the poor.

One cut in the Republican budget reconciliation package came as a surprise. It involved a former Republican president: making sure no funds are expended for the Herbert Hoover memorial. But the Republicans were even-handed. They also wiped out the Harry S. Truman memorial scholarship.