WASHINGTON — EARLIER this week, at the height of the Senate debate over the balanced-budget amendment, Democratic partisan and amateur classical scholar Sen. Robert Byrd of West Virginia rose and invoked the trials of Odysseus.
Nevermind that US politicians now seldom set their points in the context of the Trojan War. Senator Byrd, warning of what he said was the permanent damage that the amendment would cause to the Constitution, recalled the time when Homer's hero was trapped in the cave of Polyphemus. Odysseus escaped, Byrd said, by clinging to the bellies of the Cyclop's rams as they went out to graze.
''Well, senators,'' Byrd sternly told his colleagues, ''we will not have any rams' bellies here by which to ride out of this dilemma.''
At least Alphonse D'Amato kept livestock out of his historical references. When the junior senator from New York rose in support of the budget amendment, he called it the most important vote of the 20th century -- except, perhaps, for those dealing with World War II.
The amendment fight was not less than a ''war,'' said Mr. D'Amato, to keep debt from crushing ''our children.''
For most of its time in office the 104th Congress has been a story about the House of Representatives. But the spotlight shifted to the Senate this week during its showdown on the balanced-budget measure. Members seized the moment like out-of-work actors at an audition. Eloquent speeches, turned phrases, righteous tempers. High drama.
''Senators occasionally get caught up in the idea that they are making history,'' says Ross Baker, a political scientist at Rutgers University in Newark, N.J. ''Yeah, it's important. It's not often Congress gets close to passing a constitutional amendment. But is it a hinge of history? Well, it's certainly not like the Civil Rights Act of 1964, which fundamentally altered social relationships.''
Tell that to House Republican freshmen. At one point Thursday, the entire class marched across the Capitol to storm the Senate and pressure balky Democrats to pass the balanced-budget amendment.
Marching lock step in their pin-striped blues, the front guard of the Gingrich army shouted warnings of ''fiscal Armageddon.'' They were joined by their freshmen collegues in the Senate in warning holdout Democrats that, as Rep. Randy Tate of Washington put it, if they did not ''come out of the Dark Ages, they would be left in the Ice Age.''
As of press time the final vote on the amendment had not yet occurred. Defeat of the measure would mark a tactical victory for recalcitrant Democrats, who to this point have managed to frame the debate as being more about the protection of Social Security than red ink.
But Republicans might yet get strategic benefit from the battle. In the upcoming 1996 political season, they might use the amendment's defeat as a means to portray the Democratic Party as a whole as fiscally irresponsible.
Senate majority leader Bob Dole has been threatening as much, saying that he may well exercise his right to bring up the balanced-budget amendment again -- during the '96 campaign season itself.
The concept of a balanced-budget amendment, after all, is immensely popular with voters, garnering almost three-fourths approval in polls. But support declines when voters listen to details of the specific budget cuts necessary to carry out the amendment mandate.
If nothing else, Mr. Dole and his reputation for legislative shrewdness were at the heart of the balanced-budget fight.
Dole proved ''that those who lead must follow,'' says John Pitney, a political scientist at Claremont McKenna College in California. ''He had to show he was responsive to the needs of his members.
If he hadn't stepped in,'' delaying the vote for a day, ''to see if there was a chance to get the 67th vote, his members would have been very disappointed.''
In the battle of rhetoric, the Democrats clearly won. Republicans, one after another, stood stiffly on the floor or in the hallways this last week discussing the moral imperative to lift the burden of debt from future generations.
Democrats in opposition were more creative. Sen. Daniel Patrick Moynihan of New York said approving the amendment would be tantamount to adding algebra to the Constitution. Sen. Christopher Dodd of Connecticut, arguing against the measure on the floor, recalled some previous attempts to amend the Constitution.
In 1838, he noted, the nation was shocked when a congressman killed a colleague in a duel. Congress followed with a proposed constitutional amendment to ''bar individuals implicated in dueling from ever holding elective office.''
The champion of the floor during this debate was Byrd, who ended one speech by likening the balanced-budget amendment to the Gunpowder Plot of 1605.