President's task is to keep public behind him until economy picks up

How does a President who knows his economic program has not worked thus far keep up the public's confidence so that his program can work a few months from now?

That is the question, White House insiders say, that confronts Mr. Reagan and his administration.

The President is set to do everything in his power to keep this a nation of believers until spring or summer, by which time he is convinced the economy will take a turn for the better.

One thing he's clearly determined to do is remain consistent. His recent letter to Republican members of Congress made it clear, once more, that there would be no ''retreat'' on tax cuts or increased military spending. These things were a matter of ''keeping faith with the American people,'' Mr. Reagan affirmed.

The presidential strategy over the next few months comes down to this:

* In many forums - in domestic travel and on national television - Reagan will be saying that his supply-side Reaganomics will bring a change for the better, if the public will give it just a little more time.

And he will be counting on what the polls still show - that he is widely viewed as a man of good will, a man who is genuine and sincere and can be trusted - to persuade Americans that, despite the recession and massive federal deficit, he should be given a little more time to turn things around.

* The President will place the blame for the economic problems besetting the nation on other parties.

So it is that he already is attacking Congress for criticizing his budget without coming up with a credible alternative.

And he is blaming the Federal Reserve Board for high interest rates, which he believes is helping to keep his tax and spending cuts from stimulating the economy.

Further, as he pushes for more spending cuts, he will blame the Democrats for resisting him - and thus slowing down the effect of his program - by refusing to go along with his trims of social programs while insisting on less military spending than he wishes.

* And, again, the President's thesis will stress consistency - that he is staying on course, that he will not be persuaded to abandon his approach before it has had an opportunity to take effect.

This ''sticking to our guns'' approach, Reagan strategists say, is one which is already showing signs of reinforcing public and business confidence in the President.

Critics of Reagan's strategy, meanwhile, ask how long the President can ask Americans to trust him before showing them substantial results?

But Reagan strategists see this emphasis on the President's personal appeal as simply a bridge - one that is necessary so as to allow this administration to remain in good working order until, they hope, the President's program begins to lift the economy.