In the wake of yesterday's budget defeat, Democrats on the House Ways and Means Committee agreed to go back and make deeper cuts than they have so far in the spending programs under their jurisdiction.

Committee Chairman Dan Rostenkowski (D-Ill.) announced the decision and said that as a result the mark-up of the pending tax-cut bill would be delayed.

Work on this is now expected to start after the Memorial Day recess at the end of May, while the spending changes are made first in subcommittee and then in the full committee.Four subcommittees of Ways and Means, on trade, Social Security, health and public assistance, need to redo their spending plans to come up with about $2.5 billion in additional cuts.

The budget vote also affects the tax bill, as it allows $14 billion more for a tax cut in fiscal 1982 than Rostenkowski has said he wants. The Democrats on Ways and Means have not conceded that President Reagan's plan for 10 percent across-the-board cuts in tax rates for each of three years, will now pass, sources said.

Ways and Means is likely to mark up a bill costing closer to the $40 billion suggested by Rostenkowski, sources said, but the chances for such a Democratic alternative passing on the House floor may be reduced.