Immediately after Bert Lance resigned, the White House surfaced Vice President Walter Mondale as the President's new best friend. Not only a friend, but an experienced Washington figure as well, who saw the President more than anybody else and carried a writ that ran ran to all major foreign-policy as well as domestic issues.

But two weeks have shown the limits of even the best Vice President. The very qualities that make Mondale extraordinarily good in that role unfit him for the task of fixing the White House weakness that now find expression in so many of the administration's basic difficulties.

The administration's basic problem comes from trying to do too much too quickly. In domestic policy, Carter wants to solve the problems of energy welfare, inflation, unemployment, immigration, tax reform and health. In foreign policy he seeks an arms-control agreement with Russia, a settlement in the Middle East and an undoing of past wrongs in the Third World - notably in dealing with Panama, Africa, Cuba and Vietnam.

That agenda is not only formidable in itself. It is also particularly tricky because so many of the objectives are at odds with each other. Thus curbing inflation at some point comes into conflict with promoting employment. Reforming the tax system jostles the use of tax reduction as a means for stimulating the economy.

Working with Russia raises problems with the Chinese. Moving toward peace in the Middle East means getting between Israelis and Arabs.

Carter himself is not good at establishing priorities among different objectives nor choosing between opposite interests. His political stock-in-trade is embracing both conservative and liberal positions. As a functioning leader he seems to have the engineer's instinct for trying to find solutions to political and moral problems in technical detail.

So he needs help in concentrating on the important as distinct from the secondary, and in picking and choosing among rival claimants for support. Such help could come from any number of places in the President's executive office.

A strong replacement for Lance as director of the Office of Management and Budget would be of obvious use. Nobody else is better placed to emphasize some programs at the expense of others and to assert priorities on the basic questions of economic policy.

A strong White Hose chief of staff would be a surrogate for making such decisions as to who gets to use the White Hose tennis courts. Just possibly he might get President Carter to lift his head from the scrutiny of weapons systems and tax bills that all other Presidents have left to subordinates.

A strong person in congressional liaison would also serve the President well. It should at least be possible to avoid the kind of traffic jam that has energy getting in the way of taxes and taxes getting in the way of welfare.

But Mondale - though he is experienced, highly intelligent and as well motivated as anybody in Washington - cannot be much help in solving the priorities problem. Personally his great quality is the lack of a big ego. For precisely that reason he is an extraordinarily good Vice President, not threatening to Carter or his people, and able to get on well with the big shots in the Cabinet, the Congress and foreign countries.

Moreover, he is a professional politician. He does not expect to got back to a place in business or a university when the Carter administration is over. He wants to become President in his own right.

So it is typical that Mondale would enter the energy debate chiefly to ingratiate the administration and himself with the Senate establishment under Majority Leader Robert Byrd. It is equally typical that he would not sour his relationship with the President by allowing his ties to the American Jewish community to get in the way of Carter's drive for a Geneva conference.

For Mondale is the last man in the world to push the President against his native grain. No one is less likely to pull the White House together and impose upon the administration a discipline of choice. If the President really wants that, he will have to took at other people. Indeed, the best way to hurt the Vice President is to advertise him for a role he cannot fill.