The White House mounted a desperate campaign last night to revive President Reagan's tax-overhaul initiative in the face of a continuing mutiny by House Republicans and refusal of Democratic leaders to compromise.

Complicating the rescue efforts, the House abruptly adjourned for the weekend, meaning that a tax bill could not come to the House floor until at least Tuesday. House leaders said they could not promise to remain in session next week long enough to consider a tax bill before adjourning for the year.

Treasury Secretary James A. Baker III and his deputy, Richard G. Darman, spent much of the day on Capitol Hill trying to negotiate a compromise with House Republican leaders, who a day earlier organized the surprise attack that blocked consideration of a tax bill.

At day's end, House Minority Whip Trent Lott (R-Miss.), one of the original mutineers, emerged from hours of negotiations with the administration team to say, "It's on the way. We're still working and probing. It's very much alive."

More talks are scheduled today, as the administration attempts to offer concessions, including a possible letter from Reagan addressing some concerns of the House Republicans or a change in the rules for consideration of the bill, that would increase the number of members supporting tax revision.

At the end of a long day, the efforts appeared to have fallen short. Congressional sources said Reagan had secured only 34 additional GOP votes for the bill -- 16 short of the extra votes that Democrats say they need to revive the tax-revision initiative.

House Ways and Means Committee Chairman Dan Rostenkowski (D-Ill.) and Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) said they would not bring the bill to the House floor unless Reagan delivers at least 50 additional votes. The rule providing for House consideration of tax-overhaul legislation was defeated 223 to 202 Wednesday, with 164 of 182 Republicans voting against it.

O'Neill suggested that Reagan has lost his effectiveness in Congress. "When does a president become a lame duck? When he loses control over the leadership of his own party," the speaker said.

Rostenkowski said a bill could pass next week if Reagan delivers the requisite votes. But he and his task force of 25 Democrats lobbying for the bill stopped virtually all vote-garnering efforts, saying the fate of the bill rests with Reagan.

"The patient the bill is still alive," said Rep. Charles E. Schumer (D-N.Y.), a member of the task force. "The vital signs are measured."

Meanwhile, few Republicans expressed contrition over their role in undermining the chances of the president's No. 1 domestic-policy initiative of the year.

Even as Baker and White House chief of staff Donald T. Regan were meeting with House Minority Leader Robert H. Michel (R-Ill.) in search of a compromise yesterday morning, the Republicans' deputy whip, Rep. Tom Loeffler (Tex.), continued rounding up opposition to the bill in the name of the GOP leadership.

Loeffler said opponents of the bill had rallied more votes -- particularly among Democrats.

Democrats agreed that support for the bill was slipping in their ranks. Rep. Martin Frost (D-Tex.) said 20 of the 188 Democrats who voted for the ill-fated rule on Wednesday have switched sides.

"Time does not appear to be on the side of tax reform," said John Sherman, spokesman for Rostenkowski, who had talked with Reagan about strategy at several points, sources said.

Republican leader Michel, under pressure from the White House, met several times with Rostenkowski and was said by Democrats to be trying hard to find a compromise. However, Democrats on Rostenkowski's task force called the Republican proposals unworkable. The GOP leaders asked for amendments to the procedural rule that would allow the House to vote to raise the personal exemption to $2,000 for almost all taxpayers, postpone the implementation of the bill until 1987 and pay for those changes by eliminating the deduction for interest on credit-card and other consumer debt.

But Rostenkowski and his Democratic House allies said they could not begin opening the way for concessions to various groups. "This thing is like a thread on a double-knit suit," said Rep. Fortney H. (Pete) Stark (D-Calif.). "Don't pull on it or you'll be naked in 30 seconds."

The rule that was defeated Wednesday -- the one Rostenkowski and O'Neill still supported yesterday -- would permit votes only on a Republican alternative to the tax proposal passed by the Ways and Means Committee, an expanded tax credit for political contributions, two technical changes and the Democratic-controlled committee's package.

In addition to seeking changes in the rule, Republican leaders said they needed other "political cover" in order to switch their votes. Rep. Jack Kemp (R-N.Y.) proposed that Reagan vow to veto the bill unless the Senate makes major changes in it.