The Democratic-controlled House Budget Committee began work yesterday on a deficit-reduction plan that relies more on defense savings and less on domestic-spending cutbacks than a comparable-sized package approved last week by the Republican Senate.

Although the day started rancorously, some Republicans hinted at a possible compromise with the Democrats as a bipartisan majority voted to go into a rare closed-door drafting session last night.

When the committee emerged at 11 p.m. without completing its work, sources indicated that the Democrats appeared willing to give a little on defense spending to bring their package more in line with one approved last week by the Republican-controlled Senate.

The sources said that a majority of Democrats and Republicans responded favorably to a proposal, apparently by Rep. Charles E. Schumer (D-N.Y.), that would increase defense spending next year enough to cover inflation -- as the Senate proposed -- instead of freezing it at current levels, as House Democrats have proposed.

However, the Democrats' willingness to compromise on defense would carry with it the condition that Republicans support the rest of the Democratic budget package, which has no freeze on Social Security and which preserves many domestic programs that President Reagan had sought to eliminate or reduce.

Following the closed-door session, Committee Chairman William H. Gray III (D-Pa.) and the panel's ranking Republican, Delbert L. Latta of Ohio, both described it as unusually productive. The panel was to reconvene this morning to reconsider the proposal and try to complete action on the budget.

Gray said last night that the session was "simply getting a sense and a feel of where we were" and that no votes were taken. Latta said it was "a good and thorough discussion."

Both the Senate's and House Democrats' plan would cut a projected deficit of nearly $230 billion next year by $56 billion. The House plan would cut less in overall spending over the next three years than the Senate version, however: $259 billion compared with nearly $300 billion under the Senate plan.

The House Democrats' plan would cut about $20 billion from nondefense spending next year; the Senate plan would cut $30 billion.

In addition, while the Senate proposes to terminate a dozen or more programs, House Democrats would phase out only one: revenue sharing with local governments by fiscal 1987.

In most cases, from farm programs to urban aid, the House Democrats' plan would cut less drastically than the Senate plan, although even the Democrats propose to freeze or trim most domestic-spending items.

With Democrats controlling the House budget panel, 20 to 13, the Democratic-drafted plan has been expected to win approval for House floor action next week, and chances for modifications on a bipartisan basis were unclear last night. Some members said the closed-door session was aimed primarily at ending political posturing. "Politicians can't keep their damn mouths closed in front of a TV camera," said Rep. Marvin Leath (D-Tex.).

From the start yesterday, the Republicans complained that the plan was drafted in secrecy and put on track for approval with undue haste.

Slowing proceedings on the House floor with their protests, Republicans complained that they were shown the deficit-reduction draft only hours before committee action was scheduled to start.

Later, House Majority Leader James C. Wright Jr. (D-Tex.) accused the Republicans of dragging their heels in the committee as well "so we can't get to the floor next week . . . because they think we are winning."

Denying any rush tactics but delaying the session for an hour to pacify the Republicans, Gray also faced rumbles within his party over the committee's refusal to consider savings from Social Security as part of an across-the-board spending freeze.

The Senate plan would eliminate cost-of-living increases for Social Security next year; the House committee rejected this course, choosing instead to provide for a full inflation adjustment in each of the next three years