The challenge for Ronald Reagan in the next two years will be to forestall a stalemate of government. In the wake of the electoral losses suffered by his party, will he exhibit the innovation and flexibility demanded to bridge the widened Democratic/Republican split in the Congress and to resolve the severe economic problems which still beset the country after two years of Republican rule? More than ever will the worried American people be looking for bipartisan compromise and cooperation.
Neither the Democrats nor the Republicans can feel smug about the results of election 1982. Given today's massive unemployment, a Democratic landslide would not have been surprising. The Democrats did very well - but not stunningly better than an out-of-power party in a midterm contest. They could not capture the Senate, and the Congress remains divided. Thus they were not able to parlay what seemed a dissatisfied national mood into a rebuff of Ronald Reagan, although they have laid the ground for a possible return to power in 1984.
In this context, the President can feel some relief that his party did not lose more than it did. Yet it is clear that, while his mandate has not been repudiated, it has been reduced. There is no question that many Americans voted on the issue of the economy - on whether ''to stay the course,'' as Mr. Reagan put it - and voted their discontent. Republican losses were heavy above all in the industrial heart of the nation - Ohio, Michigan, Wisconsin, Minnesota. That must tell him something as he plots his future course.
Governing is further complicated. The President will probably still be able to sustain his vetoes of legislation not to his liking. But, with more than 20 additional Democrats in the House of Representatives - and most apparently not of the ''boll weevil'' variety - the Republicans will no longer have a philosophical majority in that body. It will therefore be harder for Mr. Reagan to build the kind of conservative coalition which enabled him to push through his early tax and spending cuts. He will have to forge more moderate coalitions - and this almost certainly means fewer ''supply side'' budget plans and more pragmatic, conventional Republican approaches which many of his own advisers favored from the outset.
It is also probably fair to say that the President's drive for the ''New Federalism'' - a devolution of federal power to the states - will be slowed if not postponed altogether. Democrats now control two-thirds of the state houses, and it is unlikely that those governors will be willing to have their hard-pressed states take on additional functions such as welfare or to jeopardize the existing comforting flow of funds from Washington. So, if New Federalism is to go forward, it will have to proceed in a buyers' market - not a sellers'.
If Mr. Reagan indeed adopts a more centrist course - and continues the ''corrections'' in his economic policy - he of course risks offending his more reactionary supporters. But that should not deter him. It is significant that the National Conservative Political Action Committee (NCPAC), despite a huge expenditure of money (and negative ads), was unable to defeat such targeted Democratic stalwarts and Republican moderates as Paul Sarbanes, Quentin Burdick, Lowell Weicker, and Robert Stafford. The ''new right'' apparently is not quite the political force it made itself out to be in the 1980 election. That discovery should help the President. For one thing, he need not expend energy pressing for legislation on socially divisive issues such as banning abortion.
Now that the election is over, there are urgent tasks ahead - not least of which is to bring under control the galloping budget deficits which are undermining business confidence (and willingness to borrow and invest) and threaten to frustrate economic recovery. This means grappling with social security reform and skyrocketing defense spending, two areas that could put President Reagan on a path of confrontation with the Congress. Will Mr. Reagan display the leadership, the imagination, and the tractabilily needed to avoid such a confrontation? Will the Congress display the spirit of cooperativeness, the discipline, and the political will also needed to lift the country out of deep recession?
The American people are waiting. It is time not to stay the course but to adjust it.