THE MOMENT that proved most maddening for the Republicans -- apart from the final roll call on a resolution urging the president to negotiate a comprehensive test ban -- was when Rep. Les AuCoin (D-Ore.), pointer in hand, stood up before a large, empty white canvas.

"On this chart you see listed -- in full and exhaustive detail -- every arms control achievement of the Reagan negotiating team," said this incorrigible arms-control advocate. "Here you see listed the record we're being asked to trust."

The Democrats chortled appreciatively and the Republicans ground their teeth, except those 49 who voted to tell the president, please, to talk with the Soviets about extending John Kennedy's atmospheric ban to cover underground tests as well.

The resolution was approved, 268 to 148, but has about as much clout as a prayer. It has no deadline, no teeth. It didn't make the evening news shows the night it was voted or the chat-shows the morning after. The newspapers made little of it.

But if it means nothing, it also means everything to the administration. The lobbying was intense, and at the highest level. The secretaries of state and defense were making heavy-duty calls. So was the president. Their message was a variation of the president's televised appeal for more military spending, a speech he began some ten minutes after the House had voted in favor of its modest proposal that something serious be done about the arms race.

The Reagan contention is that he has converted the U.S. from a puny international kid to the Jack Dempsey of nations. The Soviets were driven back to the conference table by the arms buildup and the threat of Star Wars. More strength, or at least much more money, will be required to extract concessions at Geneva.

AuCoin's irreverent art-show was a derisive rebuttal of administration claims that negotiations are at the "delicate" stage and could be undercut by precipitate peace moves by a rash Democratic House.

Reagan's argument was most melodramatically stated by Rep. Robert Michel of Illinois, the House Republican leader, who pictured the glee in the Kremlin on the passage of the resolution: "Would't you lean over to your aides and share the good news -- before getting on the phone with your boys in Geneva and telling them, 'Comrades, the Americans are divided. Press for the advantage. Don't budge. Drive them from the table. Get the propaganda machine in motion.' "

Republicans, unable to argue that compliance cannot be verified since Gorbachev agreed to the emplacement of seismic "black boxes" to monitor any illicit blasts, were reduced to charging that Democrats were pushing the Soviet party line. It was unarguable, since the Soviets have been observing a unlateral underground test ban since August, the 40th anniversary of the Hiroshima.

John F. Kennedy was evoked by both sides. The Republicans said that he had broken a previous test-ban pact because the Soviets had cheated. The Democrats had on their side the unassailable fact that Kennedy signed the partial test ban and said in announcing it that despite its limited effect it gave "a concrete opportunity to extend its coverage. . . to other forms of nuclear tests."

All subsequent presidents have at least conducted negotiations on the "other forms." Reagan closed them down.

Rep. Edward J. Markey (D-Mass.), who sponsored the test-ban resolution (with Democrat Berkley Bedell and Republican Jim Leach, both of Iowa), brought to the attention of his colleagues the real reason for the obdurate opposition of the administration. What the debate was all about, he said, is the president's trillion-dollar fantasy, Star Wars, the strategic defense initiative.

Reagan always calls his dream "a non-nuclear defense." But one weapon in the fiendishly complex Star Wars system -- the X-ray laser beam -- doesn't work at all without its nuclear component. The X-ray laser, which is programmed to stop incoming missiles as they course towards the U.S., requires the firing of a hydrogen bomb as a source of energy for the rays. The laser would be then targeted by a heavenly "battle station" computer to search out and destroy Soviet missiles.

Obviously, anything that intricate has to be tested. Reagan boasts that the Soviets are afraid of Star Wars, and they are. Not only does it mean they will have to make enough offensive missiles to overwhelm it, but also, they contend, it has first-strike capabilities which insure an arms race to infinity.

And that, of course, is why people who think about these things believe that no matter what the House passes, Les AuCoin's empty white chart will be operational for the duration of the Reagan administration.