AFTER A CAMPAIGN whose tone seemed unremittingly negative, the voters elected a Congress that could be capable of taking on the difficult tasks of government. The results have strengthened the hand of those in Congress who seek solutions capable of winning majority support. This may be the result of a subtle intention expressing itself in a complicated political system, or a collection of miscellaneous local results, or it may just be happenstance. In any case, it's not a bad outcome.

Consider the Senate. In a Democratic year, Republicans actually ended up with one more seat in this election than they had after the last one. That's because the New Jersey seat the Democrats picked up is the one Harrison Williams resigned; it was counted as Republican only because a Republican governor filled the vacancy. The result thus strengthens Majority Leader Howard Baker and key committee chairmen Pete Domenici and Bob Dole, the senators who fashioned the 1982 budget and tax bills when the White House and the Democrats refused to act. They provided, in advance of the election, the mid-course correction Democratic orators called for. Sens. Baker, Domenici and Dole still have a Republican majority, and one whose once enthusiastically conservative members should be chastened by Tuesday's results.

As for the House, the Democratic gains give Speaker Thomas P. O'Neill a working majority. The election produced only a few more "boll weevils," and some defectors may decide it's better to go along with the leadership. So Mr. O'Neill, with 20- odd more Democrats, should be able to produce the 218 votes needed to win on big issues in 1983. At the same time, the voters did not elect so many Democrats that the majority will fly out of control and pass measures aimed less at passage (since they would be killed in the Republican Senate) than at making a record for the next election.

The first test for the leadership of the two houses -- and for the president -- will come soon. The bipartisan Social Security Commission will meet this month, and is expected to agree on a plan by Dec. 1. The speaker said on election night that he will not allow the issue to be determined in the lame-duck session, which is understandable. But Social Security will be the first course on Congress' menu in January. Neither party addressed this difficult issue squarely in the campaign. As a practical matter, it can only be solved by the kind of bipartisan arrangement that passed the tax bill last summer. The Democrats will have to give up their charges that Republicans are gutting Social Security. The Republicans will have to stop backing away from painful but necessary changes.

Such things don't happen automatically. Neither will the accommodations and detail-work necessary for next year's budget and tax bills. Election-night statements by Sen. Baker and Speaker O'Neill suggest they are more interested in making government work than in staking out positions for the next campaign. What about President Reagan? The voters have endorsed the mid-course correction Mr. Reagan supported in fact but resisted in campaign rhetoric. Is the president prepared to do what he did in California after his party lost seats in the legislature -- to sit down with the leadership and resolve the tough issues of the day?