Now that the Senate has finally started debating the new U.S.-Soviet treaty banning intermediate-range nuclear missiles, the lawmakers face a big challenge.

That challenge is to avoid playing short-sighted political games with a treaty that could not only make history, but also give impetus to efforts to write even more far-reaching and significant arms control agreements.No political party or branch of government has a monopoly on such games.

The executive branch, for instance, is trying to insist that if the treaty isn't ratified by the time President Reagan and Soviet leader Mikhail Gorbachev sit down together May 29, a pall will be cast over the Moscow summit that could make it less productive.

What nonsense! Summits are supposed to help produce East-West harmony, not require it in advance. This treaty is far too important to be treated like a foot-race. The national interest requires that the senators seek and get clarification on any questionable points.

But that's no excuse for the foot-dragging that some lawmakers are attempting. Some of them, for example, are insisting that when President Reagan vetoes the shortsightedly protectionist new trade bill, then the nuclear arms treaty must take a backseat to efforts to override the veto. What a sorry sense of priorities that kind of thinking reflects.

Then there are those who are trying to shoot down the treaty by claiming that Moscow already has violated the pact by testing a sea-based cruise missile. Never mind that the Soviet missile is below the 300-mile limit covered by the treaty, that the test was conducted last February, or that it's impossible to violate a treaty that isn't in effect yet because it hasn't been ratified.

Come now. Let's look at the treaty in a clear perspective. Though it would not eliminate warheads, this pact would be the first to eliminate an entire class of weaponry - all U.S. and Soviet ground-launched missiles with a range of 300 to 3,400 miles. It is the first treaty between the superpowers since the 1972 Anti-Ballistic Missile agreement covering missile defenses. (The 1979 SALT II treaty was never ratified.)

The new pact also achieves a breakthrough in terms of on-site verification, including surprise inspections, of missile destruction and plant operations. Though some last minute disagreements arose between Washington and Moscow over verification and some other key provisions, Secretary of State George Shultz reports that the U.S. held firm and the Soviets in effect acceded to the American position.

Moreover, the treaty would do away with 1,700 Soviet miles compared to only 800 U.S. missiles.

No wonder the Senate Armed Services Committee, in recommending ratification, concluded that the treaty's positive features far outweigh any weaknesses.

Now the full Senate should follow that recommendation in an orderly manner, without either racing or stalling.