That's because in opposing the amendment, President Clinton and some lawmakers have argued that what's needed to balance the budget by 2002 is a will to make tough political choices, not a revision of the Constitution.
The upcoming effort to strike a bipartisan budget-balancing deal will be the chance to prove that argument - especially for returning members of Congress who oppose the amendment but want to cast a "yes" vote this year for eliminating deficits.
"The pressure is on them to be very supportive of an honest budget attempt," said Rep. Charles Stenholm, (D-Texas), a sponsor of the amendment.
"He's put in a position where it's kind of, 'Show me, Mr. President,"' Senate Budget Committee Chairman Pete Domenici (R-N.M.), another amendment supporter, said of Clinton.
The Senate continued debating the amendment yesterday, a day after Sen. Robert Torricelli (D-N.J.), sounded its likely death-knell by saying he would vote against it. Barring unexpected 11th-hour switches, that would make the final vote 66-34 for it - one shy of the two-thirds majority needed for constitutional amendments.
The Pew Research Center survey found people are hearing a drumbeat of negative news about the president but, so far, it doesn't seem to matter.
"The American public has no nerve endings," said Andrew Kohut, survey director. "They overwhelmingly told us all they hear about Bill Clinton is scandal," then gave him a thumbs up.
Overall, 60 percent approved of the way Clinton is handling his job, a record in Pew polls and up one point from one taken the week before his second-term inauguration. Thirty-two percent disapproved, also up one point.
The new survey was taken from Thursday to Sunday, amid continuing revelations about Democratic money raising but before the release of documents showing Clinton's direct involvement in offering big donors White House access.
In a USA Today-CNN-Gallup poll done after that disclosure, 42 percent said Clinton was wrong to invite large contributors to stay in the Lincoln Bedroom.
In an achingly emotional scene in Brown's court last Thursday, King's widow, Coretta Scott King, appealed to the judge to "bring some sense of closure to the pain we have endured."