President Carter told the nation's second-largest labor union today he has to "make some hard choices about how we spend the taxpayers' money. We can't afford to do everything."

In a speech to the 25th annual convention here of the United Auto Workers, Carter was plainly responding in part to charges over the last few weeks that he has abandoned potentially costly campaign promises in favor of a balanced budget four years from now.

Those charges have come from assorted liberal Democrats in Congress and such groups as the AFL-CIO. But the Auto Workers are not part of the AFL-CIO, and Carter's recital of his accomplishments so far, plus his plans for the rest of his administration, drew frequent though mostly lukewarm applause from the 3,000 delegates to this convention.

Carter insisted in his speech, as he did in the campaign, that it is possible to cut the present 7 per cent unemployment rate to less than 5 per cent by 1981, at the same time "knock two percentage points off the inflation rate by the end of 1979," and still have a balanced budget four fiscal years from now.

Carter was not specific about the "hard choices" he might make in spending, but in a later, 70-minutes talk show broadcast locally, he said he would send legislation on national health insurance to Congress early in 1978, and is committed to phasing in that major new program before he leave office.

National health insurance is a major goal of the UAW, whose outgoing president, Leonard Woodcock, supported Carter early in last year's primary campaigns.

The President's visit was a whirlwind, one-dary hop across the country in which he spend just over seven hours in California, and 11 hours in the air traveling. He left Washington at 7:30 a.m. today, and was scheduled to return to the White House shortly after midnight.

Elsewhere in his speech, his first before a labor organization since taking office, and in the talk show, where he answered 24 questions, Carter:

Accused "some powerful special interest,' including the Republican Party, of working to kill his election day voter registration proposals now before Congress "because they don't want working people to register to vote."

Maintained that "there's not a government in the world that's not trying to do a better job on human rights, partially because we've made such an issue of it.'

Said he dots not think couples ". . . ought to ever have intercourse to produce a child that's going to be destroyed by abortion. The child ought to be prevented ahead of time."

Disclosed his committee to select a new Director of the FBI has narrowed the choices ". . . down to 50 people. I understand they're going to interview 50 people."

He also said he'll decide "within a few weeks" what to do about illegal aliens, and will sign the tax cut passed Monday by Congress "within the next few days."

The crowd of UAW delegates and observers packed into the Los Angeles convention center gave Carter his warmest reception - a 50-second standing ovation - when he said he was "committed to the phasing in of a workable national health insurance system.'

On Monday Sen. Edward M. Kennedy (D-Mass.) told the same convention that national health insurance had been left behind in the Carter administration's list of priorities.

Carter spoke directly to another UAW concern in his speech - his proposal to save energy by imposing a tax on low-mileage cars and using the proceeds to give price-reducing rebates n those that get higher mileage. The UAW fears this could work against U.S. as opposed to foreign cars, and could cost jobs.

The President said "it is absolutely inevitable that we will shift to more to give price-reducing rebates on those exhaust."

"You and I have honest differences of opinion over some aspects of my proposals," the President continued. ". . . I know that you agree that the solution is not to erect trade barriers to keep out foreign competition because it only leads to trade wars, retaliation and added inflation.

"The solution lies on using our great American ingenuity to design and produce the right cars for the future . . . We can compete, and we will compete successfully." He got polite applause.

Despite his refusal to use big, gasguzzling limousines in Washington, Carter rode in a black Cadillac limousine from the Los Angeles airport to the convention center.

"Look what I came in," he said to UAW officials as he climbed out.

"Yest," said incoming UAW president Douglas Fraser, "and if it's armored, I'll bet it gets six miles to the gallon."

"We built it, so don't knock it," said Irving Bluestone, a UAW vice president. "At least it wasn't built in Japan."