INSIDE THE White House the struggle over the next budget is now beginning. The election is over, and the political people at the top of the administration are beginning to confront the unpleasant reality that -- whatever President Reagan may have thought or said during the campaign -- economic growth alone is not going to make the budget deficits go away. Mr. Reagan's lieutenants are prepared to assume that growth will be fast and steady through the end of the decade, but even on that very optimistic assumption their calculations show that the deficits only get larger. The next budget, to appear around the beginning of February, will be the president's response to this unwelcome discovery and it will set the administration's direction for all of the money questions in his second term.

The real collision here is not between a Republican president and Democratic congressmen, but among the various contending definitions of conservatism. Most of the supply-siders continue to assert, with bitter vehemence, that fast growth will solve everything. It is not Tip O'Neill but the Federal Reserve Board, with its commitment to low inflation, that they identify as their principal enemy. More orthodox conservatives support the Federal Reserve, to one degree or another, and argue that the best way to ensure economic growth is to get the deficit down first.

The first hints from the White House speak of huge (and unspecified) cuts in spending. But the Reagan administration has never been able to come up with spending cuts that begin to be large enough to balance its tax reductions and its increases in defense. It is always possible to propose, cynically, large cuts in popular social programs in the knowledge that Congress won't pass them. Alternatively, it is conceivable that the president might simply decide to stay on his present course and defend the deficits as less bad for the economy than any remedy would be. Either of those choices means paralysis.

It is highly unlikely that the country is going to get through the next four years without a recession. If that recession begins with the budget deficit already running at $200 billion a year, it will end at a far larger figure. Meanwhile, the foreign investors supporting the country's present prosperity would take fright and begin pulling their money out. That would drive the dollar's exchange rate down, and interest rates up. It's an ugly prospect, and a possibility that the budget-makers need to consider carefully.

If the people at the White House can now agree that the deficit won't simply eliminate itself, that's a good sign. The next step is to agree that any serious effort to get control of the deficit is going to have to begin with Mr. Reagan himself, and with the budget now being drafted.