Bush: No Bold Plan, but a New Tone. The White House emphasizes the federal budget cannot solve all the country's problems. THE FEDERAL BUDGET

WITH national problems piling up and little money in the federal till, President Bush is not launching any bold plan of action for the country. But he is consistently edging away from the Reagan approach with a change of tone and direction. As he begins his push for a ``kinder, gentler America,'' the President will rely heavily on persuasion and style. This week he travels out to the states to talk about his budget priorities. Today he speaks to civic and business leaders in Manchester, N.H. On Wednesday he travels to Columbia, S.C., to address the joint legislature. Still another trip is planned on Friday.

Clearly Mr. Bush is hoping to reinvigorate a sense of individual and community responsibility for problems that the federal government alone cannot fund or solve, a theme he struck in his budget message to Congress last week. ``He'll talk about how everyone should feel responsible in fighting the drug war and improving education and the environment,'' a White House aide says.

Richard Darman, director of the Office of Management and Budget, is also sending out the message that there are limits to what the budget can do. On the drug front, society needs a ``very significant cultural change'' which will not be affected by the amount of money spent, Mr. Darman told reporters last week. Similarly in education, he said, to deal with mediocrity will require a ``change in our habit of mind'' which cannot be affected by dollars alone.

``Parents are going to have to start investing more time in making their schools work and in making their homes educational institutions,'' the budget director said. ``If we don't get at some of these cultural variables, what we do in these budgets is not going to have that much effect on some of the things we care most about.''

In the wake of Bush's budget presentation, analysts credit the President with a politically deft move. By proposing some new money in such social areas as education, child care, drugs, and the environment, he has occupied the middle ground and made it more difficult for the Democrats to criticize him.

``It's true there is nothing bold or revolutionary in his budget, but he didn't run on that,'' says Stuart Eizenstat, former economic adviser to President Jimmy Carter. ``Basically he ran on keeping things going in the same direction but helping people who have fallen through the cracks.

``So that fits the public mood for moderate change with nothing dramatic, and it puts the Democrats in a difficult position,'' he says.

Given the magnitude of the budget and trade deficits and the mounting social concerns, many fault President Bush for not focusing on the nation's long-term problems and rousing Americans to an understanding of today's economic realities. Bruce Babbitt, former Democratic presidential contender, criticizes both Congress and the President for supposedly lacking any impulse to deal with world change and the issues of ``American renewal.''

But the Bush strategy clearly is to postpone talking about the ``bitter pill'' that Americans may have to swallow in future years as the deficit and debt problems persist. Meanwhile, he is adopting a respectful tone toward Congress and shifting budget priorities toward greater emphasis on social needs - a marked contrast to the approach of former President Ronald Reagan.

``He's signaled a strong desire to have meaningful negotiations with Congress,'' says John Palmer, dean of the Maxwell School at Syracuse University. ``And he's done some small but positive things from the standpoint of societal problems. Put aside the fact that taxes are not in the equation, it's a responsible and constructive budget.''

Economic analysts do not underestimate the political battles ahead, however. While Bush's maiden speech to Congress and the nation conveyed a spirit of conciliation, his budget is already drawing partisan fire, because it does not detail reductions in domestic spending.

``This is not even a one-year plan,'' says Alice Rivlin, an economist at the Brookings Institution. ``It indicates where he wants to spend more money but gives no indication where he wants to spend less. That's not quite forthright, because it really does cover up the fact that there will be quite unpleasant things that have to be done to get the things he wants.''