UNEMPLOYMENT is much too high. The House Democrats have a remedy: a billion dollars' worth of public works, to create jobs. Interest rates are also too high. The Democratic congressional leaders offer a bill to lower the rates by requiring the Federal Reserve System to pursue targets in a more congenial and accustomed range.

That's the Democrats' dilemma. The old songs are fun to sing, but they have picked up that disquieting undertone of inflation. The sponsors of each of these bills can produce a list of eminent economists prepared to assure you that this kind of legislation won't send prices up -- or, at least, it certainly shouldn't. And yet everyone, including those Democrats, remembers with unhappy clarity the experience of the Carter administration, in which this kind of policy did indeed send inflation smartly upward.

These are bills to take positions on, rather than bills by which to govern. They are the congressional opposition's equivalent of President Reagan's veto last month of the supplemental appropriation -- the one that got overridden. These gestures allow people in public office, frustrated by economic necessity, to show the public once in a while where their hearts are.

The congressional Democrats share one terrible embarrassment with the White House: neither has a theory of the economy that it trusts. Without a reliable theory of the way the economy works, it is very difficult to prescribe remedies with much confidence. Mr. Reagan came to office in the firm belief that big tax cuts would balance the budget. He cut taxes, and now the deficit is rolling up toward $155 billion a year. Until a few years ago, the Democrats all knew, as a matter of demonstrated fact, that a budget deficit stimulated the economy, generating jobs and reducing unemployment. For the past three years, they have been watching the deficit and unemployment rise eerily together -- enabling them now to denounce Mr. Reagan for both.

The House is scheduled to vote today on the jobs bill. No doubt it will pass, making everyone feel much better. Then it will disappear into the Senate where, in these last weeks of the session, its prospects are not promising. The interest rate bill is an even more difficult case. It tells the Federal Reserve to hold interest rates at a level consistent with sustained economic growth and stable prices. What level do you suppose that might be? Prices currently are far from stable, with inflation continuing at a disquieting 6 to 7 percent a year, in the trough of a recession. It sounds less like legislation than a slightly sentimental excursion into the past. The melody lingers on.