Many Democrats are expected to join Republicans and vote yes. President Clinton is officially proclaiming a "hands-off" policy, but the White House has placed intense pressure on congressional Democrats.
CBS News Chief Washington Correspondent Bob Schieffer reports that although they flatly deny it, for weeks now the president's defenders have been pressuring Democrats behind the scenes to block an impeachment inquiry.
At one point, they even tried to get Democratic senators to sign a letter saying they would never vote to remove the president if it comes to a Senate trial.
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It got so heavy handed that on Wednesday, the senior Democrat in the Senate told the White House to back off.
"I would suggest by way of friendly advice to the White House: Don't tamper with this jury . . . Don't tamper with this jury," said Sen. Robert Byrd of West Virginia.
The House Democratic leader has been telling the White House what he said Wednesday - that it's too late to stop the inquiry anyway.
"There's not a debate about whether. There's a debate about how it will be done," said Rep. Richard Gephardt of Missouri.
Gephardt and the Democrats will try to put a time limit on the investigation and confine it only to charges raised by Independent Counsel Ken Starr but they don't have the votes to get their way.
So some Democrats say they'll have to go along with the open-ended inquiry Republicans want.
"I would vote for the Democratic alternative because I think it's a preferable one, but assuming that fails, I would then vote to proceed with the inquiry," said Rep. Jim Moran of Virginia.
Vic Fazio, a senior Democratic congressman, went to the White House late Wednesday to tell the president Congress will not only approve an open-ended impeachment inquiry, but that numerous Democrats will vote for it. The only real question is how many.
CBS News Senior White House Correspondent Scott Pelley reports the president fully expects to lose the vote, so on Wednesday, the White House eased off the pressure.
Mr. Clinton told Democrats to vote their conscience. That's not a matter of principle, its hard politics. At this point, Mr. Clinton wants Democrats to do whatever they have to do to survive the election.
He'll need them a few months from now for the truly important vote, the one that decides whether Mr. Clinton is impeached.
On Wednesday morning, the president suggested that rather than eaning on Democrats, he is virtually hands off.
"I have received a large number of calls from House members and I have tried to return those calls," Mr. Clinton said. "But I think the vote would be a vote of principle. It's up to others to decide what happens to me and ultimately it's going to be up to the American people to make a clear statement there."
The White House is more active than that. Mr. Clinton only spoke of receiving calls, but later, White House spokesman Joe Lockhart said the call were "kind of 50-50" in each direction.
Advisers insists Mr. Clinton is not asking anyone to vote no. But one insider said Wednesday that when the president calls, you understand what he wants.
When asked whether it was apppropriate to pressure congressional Democrats, the president said: "I think everybody should cast a vote on principle and conscience."
Freshmen Democrats, worried about election prospects in three weeks, came to see first lady Hillary Clinton. Mrs. Clinton told them that no matter how they vote, the president will work for their re-election.
One top advisor in the president defense said the survival of the president depends on holding Democratic support for the actual impeachment vote months from now. Even then, the advisor said, it will be dicey.
In a related development, the Independent Counsel sent the House Judiciary Committee a letter saying he is not finished and he does not rule out sending them more information and more charges to consider down the road.