WHAT SHOULD people expect of the new Congress that comes to town today? We don't mean that by way of introducing a wish list of legislation or a stern instruction as to what the 97th must do. Right now the more interesting question to us is how the reconstituted Congress, with its reversed majority and minority in the Senate and its anxious, even antsy House Democratic majority gravely worried about 1982, will approach its business.

Mere mention of the Senate Democrats these days calls to mind a row of chin-on-fist Rodin figures, all of course called The Rethinker. But we suspect those ostensibly "rethinking" Democrats we have been hearing so much about are going to have to give some early and careful thought to their opposition role. It is one with which they are unfamiliar and, some would say, for which they are temperamentally breathtakingly unsuited. The tension on their side of the aisle (and in a way, within the Democratic majority in the House as well) is likely to be between the hothead, fight-everything, obstruct-wherever-you-can folks and those (soon to be called "sell-outs") who will be arguing the old Lyndon Johnson line about restraint and being seen to be helping the administration govern and not being seen to be just trippers and troublemakers. The test for the Democrats will be behaving as a tough and responsible opposition that knows when and how to fight -- as distinct from behaving as if the elections of 1980 had not occurred at all.

The Republicans promise to be more interesting to watch, at least from a clinical point of view. They -- especially Senate Republicans -- have more competing roles and loyalities and interests to accommodate. There are the claims of Congress versus those of the executive branch: how much and for how long will your basic Republican legislator identify with the purposes of the Republican administration -- and at what point might he feel more loyalty to the claims of Congress as an investigating or revenue-raising or appointee-confirming institution? Is party loyalty enough to keep him faithful to Ronald Reagan's wishes and needs? And what about the claims on him of his constituency? What does he do when Mr. Reagan backs off some of the harsher of less practical items of campaign dogma?

It is a classic self-indulgence among those whose ideas did not prevail in an election to explain that the people who got elected have no mandate to do any of the things they said they would do. We will desist from that one, but cannot keep from adding that a big burst of legislative activity on the constitutional amendment and repeal-of-civil-rights-statutes front, promised by some, would be a self-defeating and self-destructive way for the legislators to begin. It would, among other things, engage every ugly and combative emotion from the start, and also probably make it harder for the new divided Congress to gain the internal cooperation required to deal with the big one -- the economy -- that will be its greatest challenge. Sen. Mathias and Sen. Hatch, Republicans who disagree on many things, had it right yesterday when they concurred on this during a joint appearance on "Issues and Answers." "The big job before the country," Mr. Mathias said, "is to get the economy back on its feet, and I think that's what we ought to concentrate on. . . . I don't think we ought to bog down in . . . what are really peripheral issues." Mr. Hatch, while professing an intense concern for some of those issues that Mr. Mathias would just as soon see go away, did add this: " . . . until we solve these economic problems, and I think they have to be attacked intelligently and quickly, I don't see how we're going to be able to get into what I think Sen. Mathias has aptly characterized as a lot of peripheral issues."

Perhaps the key thing to watch in relation to the Congress that is assembling today is how well its two parties are able to resist temptation -- the Democrats to snipe away blindly and indiscriminately and recklessly and the Republicans to bog down in issues that divert them from the main business of economic restoration they were elected to effect.