The White House wavered yesterday in its once-confident prediction that gasoline prices would rise only 3 to 5 cents a gallon after oil decontrol.

Secretary of Energy James B. Edwards gave the estimate when the administration decontrolled oil prices Jan. 28 in keeping with a promise that President Reagan made during the election campaign. White House deputy press secretary Larry Speakes repeated this forecast last week when reporters asked about the effects of the decontrol action.

Yesterday, confronted with the information that gasoline prices already had leaped 7 to 10 cents a gallon, Speakes would say only that the administration was "hopeful" that its original forecast was correct. When Speakes was asked if he were backing down from his statement of last week, he replied wryly: "No more than I have to."

Speakes also formally announced that the president and his wife will fly to California on Feb. 19 for a four-day holiday at their ranch north of Santa Barbara.

The trip is frankly billed as one of rest and relaxation, although Speakes added, "We don't rule out having him do some work while he's there."

The day before he leaves for his home state, Reagan will deliver an economic message to Congress that is expected to spell out a program of massive budget reduction coupled with a 10 percent reduction in income tax rates.

"All but the most minute details of the president's program will be announced," Speakes said.

Reagan met yesterday with his economic advisers but put off decisions on budget cut proposals until this weekend. His aides emphasized that the proposals being circulated in the "black book" of Office of Management and Budget Director David A. Stockman are not necessarily the final versions of the proposed cuts.

As details of the budget cut plans spread, the emphasis within the administration was on speed. Reagan administration officials have been warned by a number of GOP congressmen that the president's best chance of success is to move swiftly, while he is still enjoying his political honeymoon and before opposition has time to mobilize.

An optimistic apraisal of administration prospects came yesterday from David Obey of Wisconsin, second ranking Democrat on the House Budget Committee. Obey predicted that Reagan had the votes to get 80 percent of his spending cut proposals passed.

Since liberal Democrats don't have the votes to stop Reagan's cuts, Obey thinks they should give Reagan the running room to put his economic theories to a true test instead of tinkering with administration bills. He said there would be no benefit to the Democratic Party of trying to "remake the Republican theory of economics."