The Democrats now have a "wide-open" presidential race, according to the instant wisdom formulated in the first moments after Ted Kennedy's withdrawal from the 1984 campaign. On television last Sunday, we were reintroduced to the voters of New Hampshire, as if this were the eve of their first-in-the-nation primary, instead of 15 months ahead of that blessed event.

New Hampshire will tell us, Jim Wooten said on ABC-TV's David Brinkley show, who will be president.

Hold your horses, guys. There's a question the Democrats have to answer before they pick a presidential candidate. The question is whether they are prepared to govern. And the answer to that question will be found not in the snows of New Hampshire, but in the fog of Washington.

It will, of course, be a tentative and not a conclusive answer, because two-thirds of the government -- the Senate and the White House -- is still in Republican hands.

But the practical test of the Democrats' readiness to resume the responsibility of government will be found in 1983 in the capacity of the House of Representatives to pass what is recognizably a Democratic budget.

It is no snap test, either. In the two years that Rep. James R. Jones of Oklahoma has been the Democratic chairman of the House Budget Committee, he has yet to prevail on a floor vote. It is not for want of trying.

Jones, a prot,eg,e of Lyndon Johnson who served as Johnson's last White House appointments secretary, is a legislative craftsman of some considerable skill. He is a political moderate and a hard worker who forged winning coalitions on some tax votes back in the 1970s, when he had no committee chairmanship as leverage.

But in 1981, Jones' draft budget was blasted out of consideration by Ronald Reagan's tax-cutting, defense-boosting, domestic-trimming coalition of Republicans and conservative southern Democrats. And even in 1982, when the recession was beginning to unglue that coalition, Jones failed twice to muster the votes for his Democratic budget proposal.

Now, with 26 more Democrats and 26 fewer Republicans in the new House, Jones is still not optimistic.

"As I see it right now," he told me last week, "neither a Democratic nor a Republican budget can pass the House. If they try to take it all out of domestic programs, they will fail. And if we try to take it all out of defense, we will fail. The only hope is a broadly based bipartisan coalition . . . or we're going to be in a real mess."

There is a potential for building that kind of coalition on the four-point program Jones outlined: a slowdown in the accelerated defense buildup; an increase in the revenue base; a slowdown in Social Security and other entitlement programs; and a moderation of the high-interest monetary policy.

But Reagan will not, from all signs, propose that kind of a budget. He will miss the mark by a mile on the first two points. Dogmatic Democrats will likely respond by digging in their heels against any cuts in Social Security benefits or other domestic programs. As Jones is warning, the deficits that would result from either Reagan's or the Democratic die-hards' having their way could force interest rates back up -- prolonging the recession, driving up unemployment and bankruptcies and worsening the already serious risk of an international trade war.

The rescue effort will probably be led by the Senate Republican majority, which showed early this year it is ready to challenge the president's rigidity.

The question is whether the House Democrats are prepared to contribute to the corrective process or whether they will remain spectators on the sideline, as they did this year. If, with their new 269-166 majority, they formulate a constructive budget of their own in 1983, they will find more Republicans ready to cross party lines to support it than the handful available in 1981-82. But the Democrats must settle their policy differences themselves, before they can realistically approach Republicans for help.

Their ability or inability to do so will be a fair test of their readiness to accept broader responsibilities in 1984. If they flunk the 1983 test in the House, it may not matter much what New Hampshire does in 1984.