President Reagan yesterday promised he would oppose any tax increase next year and, in a letter to a magazine, called on the American people to "work or save more than you did before" to stimulate the economy and help the nation recover from its fiscal doldrums.

"There certainly will be no change in taxes in 1982, I guarantee you," he said yesterday.

Many of the president's advisers have urged him to raise taxes to avoid huge budget deficits in 1983 and 1984 but he said that in 1982 he will only consider elimination of "undeserved tax breaks." In 1983 he said he could be persuaded to impose greater excise taxes on such items as gasoline, tobacco and alcohol.

In a "Dear Fellow Americans" letter published in the January issue of Washingtonian magazine, the president also lays the blame for federal deficits firmly in the lap of Congress, and says people should lobby their lawmakers in favor of further budget cuts to keep deficit spending down.

"The Congress still exceeds its spending targets and Big Government is not yet under control," Reagan's letter says. "We will need your continued strong support if we are to succeed where everyone else has failed."

The president flew to California yesterday, and he told reporters aboard his plane that work on the fiscal year 1983 budget, which he will present to Congress in a few weeks, is just about completed.

Noting that Americans are "shouldering the highest tax burden in our history," the president said "if the deficit continues to grow it will not be because your tax cut was too big, but because spending cuts were too small."

Reagan will spend time with family and old friends during his week's vacation on the West Coast.

In addition to daily national security briefings, Reagan expects to spend some of his vacation time working on his first State of the Union address. White House spokeman Larry Speakes said the speech is tentatively scheduled for Jan. 26.