The nuclear freeze debate in the House of Representatives, billed as an historic event and launched with the grandiose rhetoric of war and peace, has foundered in dialectic bickering.

The resolution will eventually pass in the Democratic-controlled House, all sides agree. But, cluttered with amendments and nitpicked by technical arguments, it will hardly be the clear referendum on President Reagan's arms control policy for which its backers had hoped.

"It has become a political game," said Rep. Thomas J. Tauke (Iowa), a moderate Republican. "We're trapped in sophistry."

Beneath the oil portraits of dour politicians in the lobby outside the House chamber last week, dueling charts, prepared by opposing sides, compared the range and payload of the U.S. FB111, B52H and B52G bombers to the Soviets' Backfire, Blinder, Bear and Bison bombers.

Nearby, Rep. Les Aspin (D-Wis.), a leader of the pro-freeze contingent, took a short break from the droning debate. "We're losing votes," he said. "People are getting fed up. They can't see the difference between the bill and the amendments."

He had barely finished speaking when Rep. Edward J. Markey (D-Mass.), a principal sponsor of the resolution, emerged from the chamber, looking frazzled. "Can you get back in here? We need someone to explain the difference between a Blackjack and a Backfire bomber."

No one foresaw the current quagmire when the House opened debate on the issue last month. Last year, the freeze lost by two votes. Since then freeze advocates' ranks have been swelled by the election of 26 additional Democrats, many of whom won in part because of the movement's grass-roots appeal.

Supporters were calling the issue a "motherhood" vote, a politically painless way to register opposition to "nuclear madness." Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) cheerfully said that the resolution would pass in a day by about 50 votes.

Instead, a guerrilla band of hawkish conservatives, led by Republican Whip Trent Lott (Miss.), Jack Kemp (R-N.Y.), Samuel S. Stratton (D-N.Y.) and others, has tied up the freeze resolution during 30 hours of debate over the last five weeks. Twice opponents have come within six votes of passing amendments that endorsed Reagan's arms control positions.

"We were caught flat-footed," said Reuben McCornack of the Nuclear Weapons Freeze Campaign. "We thought we could walk in and walk out with the freeze."

The resolution, sponsored by more than 200 House members, asks the United States and Soviet Union to negotiate "an immediate, mutual and verifiable freeze" on production, development and deployment of nuclear weapons.

Reagan says the resolution would undercut his Strategic Arms Reduction Talks (START) in Geneva. The administration is trying to negotiate overall weapons reductions while the United States builds its arsenal in areas the Soviets are thought to have an advantage.

As a symbol, the freeze resolution could have been a comfortable platform for any politician. Expressing bewilderment that anyone would fight over the issue, Rep. Leon E. Panetta (D-Calif.) pleaded with his colleagues, "Whether you are a hawk or a dove or something in between, you can interpret anything you want in this resolution. When you go back home, you can say anything you want to about this resolution."

Far more important than the freeze, Panetta said, will be votes on military authorization and spending bills, which contain funds for controversial weapons systems.

With Democrats using the freeze resolution to discredit Reagan, Republicans felt obligated to fight back. Their weapons are an arsenal of harmless-sounding amendments which, in the eyes of freeze supporters, would gut the resolution. An amendment sponsored by Rep. Mark D. Siljander (R-Mich.), which allowed for a freeze "and/or reductions," was defeated by a margin of seven votes.

Explaining that arms control agreements have reduced certain weapons but allowed the buildup of new and destabilizing nuclear systems, Rep. Thomas J. Downey (D-N.Y.) said, " 'Reductions' do not really mean reductions. Reductions mean more weapons."

A softer version of the Siljander amendment will be opposed by freeze advocates this week. It would allow a freeze "and reductions," rather than a freeze "then reductions," as the resolution is now worded.

An amendment to insert provisions for "modernization" of U.S. forces was fought off with a counter-amendment allowing "safety-related improvements." Freeze proponents say modernization is a code word for Reagan's military buildup.

"We're bogged down in the trenches," Aspin said. "We're arguing over words that don't have much meaning to the average citizen but have great significance to both sides."

"It takes a Talmudic scholar to discern the difference between these amendments," Downey said. Rep. James R. Jones (D-Okla.), eager for a compromise, complained, "The freeze movement brought Reagan to the negotiating table. But now that we're there, this shouldn't be a partisan issue."

Many freeze supporters who jumped on the bandwagon thinking it was mainly a symbol are not comfortable with specifics. "The freeze has always been at its best as an expression of sentiment," Aspin said. "As a negotiating posture, it has drawbacks."

Other pro-freeze Democrats, such as Albert Gore Jr. (Tenn.) and Norman D. Dicks (Wash.), want a bipartisan arms control policy that accounts for the asymmetry of Soviet and U.S. weapons systems, rather than freezing all arms.

However, with no more than a dozen members on each side dominating debate, too much political capital has been invested for either side to back down. "It's all perceptions," McCornack said. "A high school teacher from Oshkosh might read these amendments and say, 'That's okay.' But The Washington Post and The New York Times would interpret them as 'President Wins on Freeze.' "

Lott said the issue has become "a loyalty test. They don't want us to be able to say we're all for a freeze."

More than 25 amendments are still pending.

Both sides acknowledge that the resolution is likely to go nowhere in the Republican-controlled Senate. At this point, Rep. Henry J. Hyde (R-Ill.) said, "We're all weary. We want to get it over with."