Frustrated Senate Republicans bluntly warned President Reagan yesterday to expect a continuation of soaring budget deficits now that he has ruled out tax increases and Social Security constraints.

But they tacitly acknowledged that they had lost the initiative on deficit reduction as Majority Leader Robert J. Dole (R-Kan.) called on Senate budget negotiators to "get what little you can" from the House in order to pass a budget resolution before Congress leaves Friday for a month.

Senior Republicans and Democrats on the House and Senate bargaining teams resumed efforts to reach a compromise. They worked late into the night in a rare closed-door session in an attempt to get a plan for submission today to leaders of both chambers and then the full budget conference.

After the session broke up with 10 to 15 items still unresolved, House Budget Committee Chairman William H. Gray III (D-Pa.) said he was "optimistic" but added, "We still have a long way to go." Senators prodded House bargainers to cut deeper into domestic spending to offset the other savings losses.

In addition to disputes over many domestic programs, the conferees were at odds over House insistence on a further cutback in the Senate's proposal to allow an increase for inflation in the Pentagon budget.

In what was described as a "tense" and "gloomy" session with Reagan earlier in the day, GOP senators said a budget compromise was by no means assured and cautioned that, even if one is reached, it will do little to reduce $200 billion annual deficits.

There is only a 50-50 chance of an agreement, and any agreement would be "insufficient," Sen. William L. Armstrong (R-Colo.) said after the meeting. The only question is whether it would be "a half-loaf, a quarter of a loaf, a slice or crumbs," he added.

"I regret to say that the president has sold us down the river again," said Sen. Slade Gorton (R-Wash.), a Senate budget negotiator in one of the angriest comments of the day.

"This nation faces an excess of spending over revenues that will ruin our economy and cause far more hardship than any of the spending cuts being considered at this time," he said.

Senate Budget Committee Chairman Pete V. Domenici (R-N.M.) was said by colleagues to have warned Reagan "very sternly" to remember that he had been warned amply in advance when he confronts a deficit of $165 billion to $180 billion in preparing a budget next year.

"I told you so, remember, I told you so," Sen. Thad Cochran (R-Miss.) quoted Domenici as saying. Cochran said the room remained hushed until Reagan broke the silence by pledging to continue to work on the deficit problem.

The frustration and disdain with which GOP senators and some House Republicans greeted Reagan's decision Monday on taxes and Social Security continued unabated yesterday, although there appeared to be no consensus on what to do about it.

Some senators favored taking any compromise they could get, while others talked of holding out for bigger savings.

Sen. James A. McClure (R-Idaho) suggested including tax increases in the deficit-reduction package, even without Reagan's assent. But the prevailing view appeared to be that the fight was over, regardless of whether a budget accord was reached. Any compromise would be "some kind of budget Kool-Aid that's going to make us feel good but isn't going to cure the ill that the deficit is creating in this economy," said Sen. John Heinz (Pa.).

Some House GOP leaders shared the senators' dismay.

"Some of us are frustrated by the failure of the administration to do anything about deficits," said House Republican Policy Committee Chairman Dick Cheney (R-Wyo.). Asked how the president looked after his cancer surgery, Cheney said, "He looks good; he's just a little soft on deficits."

But House Minority Whip Trent Lott (R-Miss.) appeared even more frustrated at the conduct of the budget conferees. His suggested solution was to put them "in a room, lock the door from the outside and say, 'Come out with a budget resolution or die in there.' "

In a rare absence from a congressional leadership meeting at the White House, Dole stayed in the Senate, saying he had to because of the power blackout at the Capitol. "I feel powerless this morning . . . . Talk about pulling the plug, they really did it," he quipped as he opened the Senate in near-darkness.

"I guess Tip and the president are breaking out the champagne," added Dole, referring to the cheery acceptance of Reagan's decision by House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.), who adamantly opposed Social Security cutbacks and was reluctant to endorse tax increases unless they were proposed by Reagan.

Reagan's announcement on Monday had the effect of scuttling a compromise budget proposed by Senate budget conferees of both parties to cut deficits by $338 billion over three years, considerably more than in earlier plans, by raising taxes and delaying Social Security increases.

The plan included a $5-a-barrel oil import fee and biennial instead of annual adjustments in income-tax rates as well as government pension programs, including Social Security. Reagan objected to all these features.

After the White House meeting, spokesman Larry Speakes said the president urged passage of a budget this week and said the House should "meet the Senate on domestic savings in order to have a credible budget compromise."

But Dole expressed doubt that major domestic spending cuts would be made over the long term, noting that about half the total savings in the House-approved budget comes from defense spending.

Acceptance of this kind of proportion would mark a setback for the president, who wanted to increase military spending 6 percent above inflation while freezing, cutting or in some cases eliminating domestic programs. In stressing the importance of domestic spending cuts during his meeting with congressional Republicans, Reagan was reported to have talked about a woman who supposedly missed an examination for Medicaid or Medicare because she was at a travel agency booking a ticket to Honolulu.