He has been under investigation for two years, accused of misusing his expenses as a result of the so-called House post office scandal. Denying that he has done anything wrong - and certainly nothing that others did not do - Mr Rostenkowski has already voluntarily paid the government back dollars 82,000 (pounds 54,000).
Lawyers for Mr Rostenkowski, a Chicago Democrat, and federal prosecutors were said yesterday to be close to a deal which must be be announced before 31 May. The critical issue is whether Mr Rostenkowski will go to jail and, if so, for how long. Prosecutors insist they will not agree to any bargain which does not include prison.
The fall of Mr Rostenkowski is a serious blow to President Clinton and the ability of the Democrats to force health care reform through Congress. His successor, Sam Gibbons, will not have the same authority as Mr Rostenkowski as chairman of the Ways and Means Committee.
If the plea bargain falls through at the last moment, the prosecutors are likely to indict Mr Rostenkowski on multiple counts by Tuesday. This would threaten him with a long and costly trial at the end of which he might go to jail on several counts of embezzlement or theft.
The scandal started in 1991 with an inquiry into petty corruption in the House post office but has gradually broadened into an investigation of how he used his official position to make money through 'sweetheart' deals and the padding of office expenses. Prosecutors earlier this year agreed a plea bargain with former head of the House post office, Robert Rota, who promised to testify against, among others, Mr Rostenkowski.
Mr Rostenkowski believes that he has not done anything wrong during his 35 years in Congress but his opponents say that he has never abandoned the big city machine politician's willingness to benefit from graft. A trial could go on for three years and cost Mr Rostenkowski dollars 1m (pounds 666,000). Republicans are waiting to attack any bargain which seems too lenient.
Other bad news for the Democrats, who have long dominated the House of Representatives, is the loss of a seat in Kentucky which they have held for 127 years.
The loss is ominous because it is one of a large number of seats in the border and southern states now veering towards the Republicans.