WASHINGTON -- Supporters of a constitutional amendment that would give Congress the power to outlaw flag burning have their best chance ever to win Senate approval later this month.

Although the House has passed such a proposed constitutional amendment six times during the past decade, it has always died in the Senate.

The Senate is slated to try again in two weeks -- right after Flag Day and just in time for July 4 -- and the margin is expected to be razor-thin.

''I've sweated bullets on several occasions on this, but this one is as close as it can get,'' said Paul McMasters, a scholar at the First Amendment Center in Arlington, Va., and a leading opponent of the proposal.

Based on public pledges and prior votes on the issue, 34 senators are expected to oppose the amendment and 66 -- mostly Republicans -- are expected to back it. That would put the amendment within one vote of winning the two-thirds majority of everyone ''present and voting,'' or 67 senators, if all 100 members participate.

The last time the chamber considered the proposal, in 2000, it was defeated 63-37.

Because the margin now is so close, the outcome ultimately could hinge on who is present when the roll is called, McMasters noted.

''If one or two opponents are out sick or on a trip, the 66 votes (of supporters) could do it,'' he said. Or, if a wavering senator decides to back the amendment, and there are no other changes, the proposal would pass.

Both sides are planning dueling news conferences on Flag Day, this Wednesday. The Senate debate on the proposal is set for June 26. The House already passed the amendment last June by a vote of 286-130.

In addition to two-thirds majorities in the House and Senate, amendments must win approval in three-quarters -- or 38 -- of the states before the language can be added to the Constitution. State ratification appears to be assured because all 50 states have passed resolutions against burning or otherwise desecrating the U.S. flag.

The push to amend the Constitution and specifically allow Congress to bar flag desecration began after the Supreme Court ruled in 1990 that a federal law outlawing flag burning violated the First Amendment because the action constituted a protected form of speech.

One of the cause's biggest champions was the late Rep. Gerald Solomon, R-N.Y., who sponsored similar flag-protection amendments before retiring from the House in 1998.