With a rhetorical bow to the "mandate of the people," Senate Minority Leader Robert C. Byrd (D-W.Va.) predicted yesterday that the Senate will approve "most of the spending cuts" recommended by the Reagan administration, as well as some version of a tax cut, by next August if not sooner.

He repeated his earlier attach on the president's three-year tax cut proposal but added that "some of us may be willing to go along with a one-year across-the-board tax cut" as the administration wants. "But there is no consensus on that yet."

Byrd spoke with reporters at his customary Saturday morning coffee clatch, a ritual carried over from his days as majority leader. Thanks to a dispensation from the new Republican Senate leadership, he also still occupies his same ornate office, with its vaulted ceilings, crystal chandeliers and liberal gilt.

Byrd, in a champagne-colored sports shirt, also indicated approval of the special fast-track packaging of the proposals, as advocated by the administration, under a process called "reconciliation." This will enable the Senate to lump most of the proposals together and act on them within a statutory time limit.

"If it all comes up in little pieces," Bryd said, "it will be nickeled and dimed to death. The president won't get his program and the Democrats will get the blame."

He noted drily that he had helped work out the budget reforms that make this procedure possible. "The majority ought to be able to work its will. Of course, at the time I was thinking of the Democratic majority . . ."

In line with the Democrats' strategy of limited resistance on selected Reagan proposals, Bryd reiterated a determination to keep the poor and working people from taking it on the chin. Reagan's tax cuts, he said, favor the rich and also are inflationary. He indicated, however, that Democrats would support tax incentives for business investment and increased productivity.

Byrd, who is up for election in 1982 to a fifth six-year term, also defended several federal programs on the Reagan hit list which he said had been "very beneficial to Appalachian states," such as benefits to black lung victims, the Economic Development Administration and the Appalachian Regional Commission.

When a reporter reminded him he has "only 46 members," Byrd responded by repeating incredulously, "Only 46? Only 46? Only 46? Only 46? Why, I've read of a man who only had 12 disciples."

There will no doubt also be some Republicans "aghast" at some of the Reagan proposals, he added, who can be expected to join the Democrats in the loyal opposition.