House-Senate budget conferees groped inconclusively for a way out of their impasse over domestic spending yesterday amid warnings that time is running out for compromise on tax and spending targets for next year.

As the conferees ended their first week without agreement on any major budget element, they held out hope for an accord, especially if they can resolve terms of a "contingency fund" to incorporate House proposals for new domestic spending to alleviate the effects of unemployment.

Several sources suggested that previously more controversial aspects of the budget, including taxes and defense spending, may fall into place if the conferees can assuage conservative and liberal fears over how the contingency money will be handled in the budget.

That hurdle may be difficult to scale. Liberals are reportedly fearful of any special "second-class" treatment that might undercut shaky chances for passage of their anti-recession programs, while conservatives are reluctant to give what they regard as a blank check for more social welfare spending.

House Budget Committee Chairman James R. Jones (D-Okla.) said conferees have agreed in principle to put the new spending, estimated at anywhere from $7.6 billion to $11.6 billion, into a contingency fund to be spent only if programs are authorized. But other details have yet to be worked out.

At mid-afternoon, the conferees broke off formal negotiations to try to work out the contingency fund privately. They are scheduled to resume deliberations today.

But Jones warned that the budget conference is approaching a "crossroads," and Lawton Chiles (D-Fla.), ranking minority member on the Senate Budget Committee, said: "What we do in the next 24 hours will tell whether we have a budget for next year or not."

On taxes, given scant attention in formal conference sessions, sources indicated that private talks are centered on a compromise ranging around $9 billion to $12 billion for next year, although no decisions have been made.

Even though such compromise figures are vastly closer to the Senate-approved figure of $9 billion than to the House's figure of $30 billion, senators have warned that even a slight increase could jeopardize Senate approval of a conference compromise in light of the Senate's razor-thin vote for its own version of the budget last month.

The House has similarly difficult problems with spending, especially for social welfare programs, one reason why the contingency fund is regarded as a key to unlocking the budget problem. "It won't solve the whole problem, but the problem can't be resolved without it," a conferee said.

Another suggested that the problem is compounded by increasing pressure within moderate-to-conservative House circles for some type of spending "cap" to go along with the House leadership's drive for an income limit on the scheduled July 1 income tax cut.

This pressure could increase, some sources said, especially if the conferees produce a budget compromise that is defeated on the House floor. A major reason for the conferees' difficulties is negotiators' fear that a compromise could be defeated in either chamber because of ideological and partisan differences in the makeup of the two bodies.

The problem was underscored yesterday when Rep. Delbert L. Latta (Ohio), ranking Republican on the House committee, objected to the contingency fund even though Senate Republicans such as Budget Committee Chairman Pete V. Domenici (N.M.) are pushing the idea. Jones has said repeatedly that Republican votes are needed to pass a compromise in the House.