Rep. Bill Gradison represents Cincinnati, including Pete Rose, so he is used to living with large numbers. However, he is determined to see one large number -- the federal budget deficit -- shrink. He has contributed to the creation of a National Economic Commission that may help the next president succeed in what may be, effectively, his four-month term.

Yes, four months. One reason for the commission is this lesson from the Reagan years: presidents must strike while the iron is hot, and many elections do not even heat the iron -- do not, that is, create a mandate. By September 1981, Reagan was, in domestic policy, a spent force. This was so even though the Electoral College had done its duty in 1980, exaggerating the electorate's decisiveness, giving Reagan 43 states from barely 51 percent of the vote.

It is unlikely that any current candidate will receive more of a mandate. The government's composition reflects the electorate's ambivalence: the president and Congress have different priorities. The public endorses cutting government in general and almost nothing (other than welfare and foreign aid) in particular. In 1984, there was a landslide without a mandate, and in 1988 there is apt to be neither a landslide nor a mandate. Thus the next president's window of opportunity for decisive action may be as narrow as four months.

The job of a commission such as the economic commission is to provide momentum for painful recommendations and to provide political cover for those who enact them. The encouraging model was the Social Security task force of 1982, which began the process of raising Social Security taxes and limiting benefits.

But that task force had a single sharp focus, and there was a clear crisis: the trust fund was running dry. Regarding the budget deficit, there are serious people who argue that it is not a crisis. And those who agree that it is a crisis disagree about appropriate cures.

Gradison notes that it took years, and a stock-market spasm, to produce last autumn's economic summit between the president and Congress. And, says Gradison, it failed on two, perhaps three, crucial matters. It did not cut spending, which will be higher this year than last; it did not cut the deficit, which will be higher this year than last; and it probably did not prevent the automatic Gramm-Rudman across-the-board ''sequester'' (cuts) due on Oct. 1, 1988. That sequester may not occur, but only because there may be a bipartisan wink -- a tacit agreement to fudge the deficit figures, thereby preventing budgetary bloodshed five weeks before Election Day.

The commission's first 12 members must be selected by March 1. Two more, one from each party, are to be added by the president-elect after Nov. 8. The commission is to report its recommendations by March 1, 1989.

The six Democrats have been picked: Rep. Bill Gray of Philadelphia, chairman of the House Budget Committee; Sen. Pat Moynihan; Robert Strauss; Lane Kirkland of the AFL-CIO; Felix Rohatyn, the financier; Lee Iacocca.

Republicans are concerned about the cost of entitlement programs. They are worried about Moynihan, a key member of the Social Security task force. He is running for reelection this year, has been philosophically fierce in criticizing Reagan's fiscal policy, and is expected to resist cuts in entitlement programs. Republicans regard all the Democratic members as intellectually serious but also (and for that reason) problematic: their recommendations will have a distinctly Democratic cast. Therefore, the Republican side must be assembled with cohesiveness in mind.

Senate Minority Leader Bob Dole, House Minority Leader Bob Michel and President Reagan each has two choices. Dole is certain to pick Sen. Pete Domenici of New Mexico, ranking Republican on the Budget Committee. Former transportation secretary Drew Lewis, the GOP's utility infielder, is on many lists. Republicans surely will have the wit to choose at least one woman -- former ambassador Anne Armstrong; former HUD secretary Carla Hills; Mariana Whiteman, a General Motors vice president; Nebraska Gov. Kay Orr.

Others on the lists include Charls Walker (an advocate of consumption taxes); Bob Beck, chairman of the board emeritus of Prudential (another veteran of the Social Security task force); former governor Lamar Alexander; California Gov. George Deukmejian (who might have to leave the commission to run for vice president). The man who would give the commission special weight is, of course, Paul Volcker.

Today this commission is just a cloud on the horizon no larger than a man's hand. But it may matter very much 12 months from now, when the next president is in the first of what may be a very few effective months.