The issue is an indication that whatever happens to the President in the Monica Lewinsky affair, Mr Clinton's foes are intent on pressing ahead with other investigations that could lead to criminal indictments for some of the Clinton allies.
It is also a sign that the Congress may want to examine not only the President's sexual misbehaviour and his alleged attempts at a cover-up, but the whole array of charges that stretch back to the Whitewater land deal.
Republicans want Mr Lindsey to testify before Kenneth Starr's grand jury, but he has argued that he is shielded by attorney-client privilege.
A court has rejected this claim, and it is pending before the Supreme Court. Until this issue is settled, there is no question of striking any deal to limit the impeachment process against the President, Republicans have told the White House.
Mr Clinton's supporters want to limit the time for this process and are holding out the possibility of accepting some lesser punishment than impeachment.
The response from Republicans in the House of Representatives has been cool, partly because they see no reason to hold back from impeachment. But they also see little interest in striking a deal until the White House co-operates on other issues, such as that of Mr Lindsey.
He is not a symbolic figure in this argument; as an old friend of the Clintons, he has been involved in a number of the other issues thatMr Starr is investigating.
Mr Starr continues to examine the Whitewater land deal; Travelgate, which involves the manipulation of jobs in the White House travel office; and Filegate, the alleged misuse of White House files.
He wants to prove a broader pattern of obstruction of justice by the White House, and Mr Lindsey could be a key witness.
The House judiciary committee has yet to establish the process for impeachment hearings, but is likely to do so within the next two weeks.
This would be followed by the hearings themselves, which would culminate in a decision on whether to impeach the President.
A decision on whether to begin hearings is likely on 9 October, committee aides said yesterday, but they would not start until 3 November, after the Congressional elections. That means that a final decision is unlikely before next year.
The committee will meet today to discuss the release of further documentation from the Starr inquiry.
Mr Starr sent a report and boxes of supporting documentation to the committee, but so far only a small percentage has been released.
The remaining evidence may include transcripts of Ms Lewinsky's conversations with her former friend, Linda Tripp, tapes of which have now become the subject of investigation after some were alleged to have been duplicated and edited.
The Republicans are sounding distinctly lukewarm about the next phase of releasing documents, partly because some - such as the Tripp tapes - may be seen as favourable to the President.
"I'm advised by staff that this isn't going to contain much sensational material. We're still reviewing over it," said the Republican Congressman Bill McCollum.
The White House is clearly recovering its confidence. Though a deal is still only a small possibility, Democrats in Congress are being mobilised to fight for the President and Mr Clinton has spoken to members of both parties in the past few days to build support.Reuse content