Is the President testing waters for bipartisan budget compromise?

There are hints that the budget impasse may be breaking.

President Reagan is allowing his chief of staff, James A. Baker III, to begin a dialogue with Democratic congressional leaders on what can be done to move his budget forward.

Does this mean Mr. Reagan is prepared to move toward an accommodation? There are those within the administration who say this now is possible - though the President isn't ready yet to move away from his intractable public negotiating position.

The President's director of communications, David R. Gergen, emphasizes that ''Jim Baker has authority to listen (to the Democratic congressional leaders), but not to negotiate.''

If the President can find ''satisfactory give'' on the part of Democrats in Congress, insiders say, he may be willing to consider an alternative budget package.

Why is Reagan now permitting the ''opening of lines of communication with Congress'' - as one aide puts it - on this issue?

For several weeks now, some high-level administration people have been saying that Reagan would move away from his adamantly held position if he could find a compromise that was acceptable.

This Reagan move was earlier envisioned by some around him as probably coming sometime in May or even June. But now that timetable has been revised.

The prime mover in getting White House talks with the Democratic leaders started was GOP House minority leader Robert H. Michel of Illinois.

Congressman Michel got the word to the President that ''it is very important that we not lose touch with the Democrats in Congress.'' Out of this came the President's authorization for Sen. Howard H. Baker Jr. (R) of Tennessee to talk by telephone with House Speaker Thomas P. O'Neill (D) of Massachusetts.

Opinion polls, which indicate much of the public feels the President is being too ''hard nosed'' in fighting for his budget, may have helped to persuade Reagan to at least begin sending out feelers to Congress.

But, additionally, Republicans from all around the US are telling the President that he must end the impasse, lest a stalemate occur that might keep the recession from ending - or even plunge it into a depression.

All this does not mean that the President is ready to concede he is budging. He still talks of not giving an inch on his defense budget and three-year income-tax trims. In fact, Mr. Reagan will likely retain his public negotiating position for quite a while - waiting to see whether his private feelers bring a response indicating an acceptable compromise might be worked out.

In the last few days the Monitor has contacted Republican state political leaders from every geographical region. These politicians were saying:

* It is time the President take the initiative on his budget. He must begin to work out some kind of a package with Congress.

* The continued impasse on the budget is adding to business uncertainty - and this is doing nothing to lift the recession.

* This delay is more damaging to Republicans than Democrats.

* Above all, a stalemate must be avoided. The President won't be able to blame the Democrats if this happens, particularly if the result will be a drag on the economy. Instead, he and Republicans generally will be criticized for letting the country drift.