Despite claims of progress in White House-congressional budget negotiations, major roadblocks emerged yesterday in the two Senate committees that are taking the lead in trying to assemble an alternative to President Reagan's unpopular budget for next year.

Bipartisan opposition surfaced in the Senate Finance Committee to creation of a new corporate minimum tax--a key element of both administration and congressional revenue-raising drives. And Sen. Russell B. Long (D-La.), perhaps the most skillful tax legislator, declared his strong support for corporate tax sale provisions, giving proponents of the controversial section of the 1981 tax act a key ally.

In the Senate Budget Committee, several Republicans declared that Congress should not wait for tax and spending concessions from Reagan, but Sen. Ernest F. Hollings (D-S.C.) warned even more bluntly than before that Reagan has to move first if Democrats are going to support a compromise. "He's going to have to lead . . . to admit he has a problem," said Hollings.

These warning signs of future trouble emerged as both White House and Senate Republican leadership sources said that talks between congressional Democrats and White House chief of staff James A. Baker III are going well and may produce enough of a consensus to break the budget logjam by Easter. Democrats appeared less optimistic.

A Republican congressional source said the talks are pointing toward only modest savings next year, adding up to a fiscal 1983 deficit that can probably not be kept under $100 billion. The major emphasis would be on deficit reductions in future years, including substantial cuts in benefit entitlement programs, the source said.

The Budget Committee served notice it will begin work on the specifics of a budget resolution April 13, with most Republicans present at yesterday's meeting saying they wanted to proceed regardless of whether the White House is ready. "I don't think we ought to wait for the president," said Sen. William L. Armstrong (R-Colo.), adding that delay would amount to a "cop-out." "We could still be here waiting in July," complained Sen. Slade Gorton (R-Wash.).

Chairman Pete V. Domenici (R-N.M.), analyzing a half-dozen alternative budget plans that committee members have submitted, said they generally agree that defense and entitlements should be cut and revenues raised "significantly more than the president has proposed"--producing a balanced or nearly balanced budget by fiscal 1985.

Hollings said he, like the Republicans, was ready to vote but added, "The question is how we get the votes." He later told a reporter: "I don't see anything this Draconian and traumatic succeeding unless the president changes his mind on whether he has a problem. He has a problem, the country has a problem--but he won't admit it." Even though enough Democrats could be won over in the Senate, the Democratic-controlled House will not go along without Reagan's leadership, Hollings said.

At the Finance Committee, two members--Sens. Malcolm Wallop (R-Wyo.) and Steven D. Symms (R-Idaho)--declared their unwillingness to support any tax increases this year.

But, perhaps more importantly, the committee session was marked by varied attacks on tax increases, signaling the election-year difficulty of martialing a majority of the 20-member panel behind any tax hike.

Sen. Lloyd Bentsen (D-Tex.) led a detailed denunciation of the administration's proposal to significantly broaden the corporate minimum tax to raise a total of $7.1 billion in 1983 and 1984.

Bentsen contended that the proposal, which would hurt many of his state's oil and gas interests, would "take back 52 percent" of the corporate tax breaks enacted last year. The administration proposal would require corporations using tax loopholes to pay little or no federal tax, to pay at least a minimum amount based on a complex formula.

Sen. Robert J. Dole (R-Kan.), the committee chairman, has proposed repeal or severe restriction of the corporate tax leasing allowed under last year's legislation, but yesterday it became apparent that he will have a head-on battle against Long, the panel's ranking Democrat.

Long contended that the 1981 Economic Recovery Tax Act gave profitable businesses a subsidy for new investments which would be unfair to deny to unprofitable firms by killing tax leasing.

Repeal, he said, would be to put "a tax subsidy on the basis that those who need it the most don't get it, and those that need it least get it. That's totally unfair."

The administration continued to defend tax leasing, although Assistant Treasury Secretary John Chapoton said some modifications may be recommended after the department completes a study of 20,000 lease deals that took place in 1981.

Congressional sources told the Associated Press that negotiators for the administration and both parties in Congress are discussing a reduction and delay in this year's Social Security cost-of-living increase as part of the compromise to reduce budget deficits.

The sources said an oil import fee also is being considered as part of a plan to raise taxes by as much as $30 billion. A $5 billion cutback in Reagan's Pentagon budget and a reduced pay increase for federal employes also are under consideration, the sources added.

These sources, who declined to permit use of their names, stressed repeatedly that no decisions have been made in the private discussions involving White House chief of staff Baker, White House congressional liaison Ken Duberstein and Republicans and Democrats from both houses of Congress.

The sources told AP that the negotiators are considering a plan to limit cost-of-living increases this year for Social Security to 4 percent and to delay them by three months to Oct. 1.

Normally, the increase would be the same as the increase in the consumer price index from the first quarter average for 1981 to the first quarter average for 1982, expected to be roughly 8 percent.

The same changes would be applied to other benefit programs, presumably including pensions, AP reported. Taken together, these changes would save roughly $11 billion, officials said.

Also under consideration is a proposal to cut the pay increase for federal employes to 4 percent this year instead of 5 percent and delay the raise for three months, AP reported.