WASHINGTON (AP) _ Hailed by some as medicine for the deficit, cursed by others as poison for the Constitution, the balanced budget amendment faces a lengthy airing in a Senate where neither side is certain of victory.

''We cannot simply and constantly go into debt,'' Sen. Paul Simon, D-Ill., said Tuesday as the Senate launched its long-awaited debate on the amendment.

Sen. Robert C. Byrd, D-W.Va., leading the opposition, noted the system of checks and balances built into the American system of government and said: ''Put this in the constitution and we tear all that down. ... We're about to fool the American people. They're being misled.''

A full day of debate was set for today on the measure, which requires a two-thirds majority of both houses to be sent to the states for ratification. A final vote may not come for two weeks.

The amendment would require a three-fifths vote of the House and Senate before federal spending could exceed revenue in any year. A separate three- fifths vote would be required to approve an increase in the public debt if there were inadvertent deficit spending.

The requirements would go into effect in 2001 and be waived in the event of a declaration of war by Congress.

While the amendment would require a balanced budget, it doesn't specify how one would be achieved. That would be up to lawmakers, although it would be tougher to raise taxes than to cut spending, since the amendment requires a majority vote of the total membership of the House and the Senate - as opposed to a majority of those voting - to raise taxes.

Both sides are marshaling a variety of weapons to sway the public.

The National Taxpayers Union has purchased a small amount of radio and television time to support the amendment; the Clinton administration last week released an estimate of the toll that deep spending cuts would take on states and their residents.

A weekend survey by The Associated Press indicated that a dozen undecided senators will determine the fate of the amendment. Two of them - Democrat Barbara Mikulski of Maryland and Republican Nancy Kassebaum of Kansas, have since declared their opposition.

Two others, Democrat Sam Nunn of Georgia and Kent Conrad of North Dakota, expressed misgivings about the impact the amendment might have, but said Tuesday they remain uncommitted. Another, Sen. Pete Domenici, R-N.M., said he is drafting an amendment to limit the power of federal judges to impose deficit solutions on Congress in the event of a deficit. Sen. Larry Craig, R- Idaho, a backer of the balanced budget amendment, said he's amenable to such a change, provided other key supporters are.

In an interview, Craig vowed to fight all other amendments on the theory that they are designed to kill, rather than strengthen the balanced budget amendment. Several supporters of the amendment said they believe Byrd, a master of the Senate's arcane rules, has prepared about 30 politically enticing changes that could doom the provision if adopted.

Byrd could not be reached for comment, but instead, outlined his case in the opening round of debate round of debate on Tuesday night.

''We're acting like Samson, taking the pillars of the Constitution in our arms and pulling down the whole structure,'' he said, adding that his opposition represented ''one of the most important votes I have cast in 41 years in Congress.''

Supporters said change was essential. ''I believe we have to get this amendment in place to ensure that there will be an end to the long spending binge in Congress,'' said Rep. Orrin Hatch, R-Utah.