President Carter acknowledged yesterday that the nation would be faced with '"serious" inflation for at least the next few months.

Carter, in remarks transmitted to the National Cable Television Association convention in Las Vegas, urged support of his voluntary anti-inflation guidelines. "We've just got to stick to them," he said.

The President's remarks came as Federal Reserve Board Chairman G. William Miller told Congress that while the White House program was showing some results it would take the nation six or seven years ot win the war against inflation.

Carter said compliance with the wage-price guidelines has been "remarkably good."

Two positive economic signs pointed to by the President were a slowdown in the economy and the strengthening of the dollar overseas. Carter claimed both were signs the anti-inflation program was working.

Carter said the dollar has stabilized so much on foreign money markets that U.S. allies "like Japan and West Germany are complaining it's too strong." As for the nation's economic growth rate, Carter said it was "slowing somewhat."

Miller, testifying before the House Ways and Means Committee, said "it is may personal judgment that we have had lower price increases than we would have had without (the guidelines)."

Miller said a combination of federal spending restraint, the White House wage-price guidelines and Federal Reserve Board monetary policy should reduce inflation by one-half to three-quarters of one percent a year.

But a control inflation without triggering a recession, Miller said, would take six to seven years.