President Reagan cast himself as being in a "epic conflict" with the House Democratic leadership over his 1983 budget, and told about 1,100 California Republicans at a fund-raising dinner here tonight that his 1980 mandate to control federal spending is hanging in the balance.

Appearing far from certain that he will prevail in the budget fight on Capitol Hill this week, Reagan telephoned wavering members of Congress from Air Force One as he flew here from Washington this morning. At the $1,000-a-head dinner he kept up a drumfire of criticism of House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.).

O'Neill wants to "cancel the election of 1980" and return to the "old days of ever-bigger taxes and uncontrolled government spending," Reagan said.

"We are engaged in an epic conflict with the proponents of negativism, the advocates of 'no,' " he said. "They offer the politics of no growth, no take-home pay, no neighborhood schools, no incentives to work, no incentives to save, no protections for the family and no security for our nation or safety at home."

Deputy White House press secretary Larry Speakes said Reagan had talked with about five congressmen, mostly Democrats, to urge them to support a Republican-drafted budget alternative that will be voted on this week.

Speakes said GOP congressional leaders had given Reagan "encouraging" reports on the bill's chances at a meeting at the White House before he left. But, Speakes said, "It's going to be close. It's going to be right down to the wire."

Speakes also announced that the president today sent to Congress a request for supplemental appropriations of $29 million for fiscal year 1983 to get nine new water projects started, which Speakes said were the first such projects recommended by a president in three years.

The projects would be in Arkansas, Hawaii, California, North Carolina, Texas, Virginia and Iowa and two in Oregon.

On arrival, the president stopped briefly at the Rockwell International space facility, prime contractor for the design of the space shuttle's main engine, before his speech to Republicans at the Century Plaza Hotel.

About 4,000 of youthful demonstrators espousing a wide variety of causes gathered in front of the hotel before Reagan's speech. Kept away from the hotel by mounted policemen, they carried signs saying "ERA Yes," "Reagan, Assassin of Peace," "Malvinas Belong to Argentina," "Stop Reagan's Raw Deal Economics" and "No More Financial Aid Cuts."

After the speech he was to fly to his 688-acre vacation retreat, Rancho del Cielo ("Ranch in the Sky"), overlooking the Pacific Ocean about 30 miles north of Santa Barbara. He and Mrs. Reagan are to remain there until Sunday.

Speakes said Reagan would work on drafts of speeches he is to give in Europe next week and would study three briefing books to prepare for the trip. Speakes said the president also intends to make more telephone calls to members of the House from the ranch Wednesday.

Workers at the Rockwell plant cheered Reagan, waved small American flags and seemed only to want to know whether he planned to continue to spend money for space and defense programs. In addition to the space shuttle, Rockwell has been awarded the contract to build the B1 bomber.

Reagan told them that the administration planned to proceed with plans for four space shuttles and that a fifth was under consideration.

Nearly 40 percent of all aerospace jobs in the nation are in California, and the industry is booming. However, overall unemployment in the state rose to 9.4 percent last month, reflecting layoffs at auto and tire plants and depressed housing and retail industries.

Reagan aides said repeatedly that the key to recovery is in getting interest rates down. On the flight here, pollster Richard Wirthlin said lower interest rates also were the "linchpin" for raising the president's job-approval rating.

Wirthlin said he thought it was possible that the European trip would improve Reagan's ratings in the polls, but that "I don't think it will dramatically break the doldrums we're in now.