The US Attorney-General, Mr John Ashcroft, says he is "deeply concerned by the slow pace" of emergency legislation in the Senate.
But the Senate Judicial Committee's redoubtable Irish-American chairman, Mr Patrick Leahy, who has often sparred with Mr Ashcroft, is not for moving. The Vermont Democrat acknowledges the national mood to tighten up legislation and sympathises, but he says they are not going to be rushed and get it wrong.
While in the House the bipartisan spirit has held, the Senate Democrats have not been willing to roll over and Mr Leahy counterattacks by accusing the Attorney- General of reneging on an agreement reached on Sunday after many hours of negotiation between the committee and the White House.
The main cause of the hold up is provision in Mr Ashcroft's legislation allowing the FBI to share wiretap and grand jury information with other agencies, the CIA and the National Security Agency, without a court order.
The current restriction is a product of concerns that such information might be misused to discredit political opponents and Mr Leahy had insisted on the requirement of a retrospective court order - a compromise Democratic aides claim was acceptable to the White House on Sunday.
In the House, with its Republican majority, agreement has been forthcoming but not on Mr Ashcroft's full agenda.
The House legislation strengthens the hand of investigators in several areas, including their ability to conduct electronic surveillance in anti-terrorism cases.
It also stiffens penalties for several terrorist offences, and extends the statute of limitations on terrorism cases.
The legislation also would allow law enforcement authorities to obtain nationwide "pen register" and "trap and trace" orders that permit them to learn the incoming or outgoing phone numbers from a particular telephone.
In addition, the law also extends the amount of time for which a court order may be used to conduct physical searches and electronic surveillance under the Foreign Intelligence Surveillance Act, from 45 days to 90 for physical searches and from 90 days to one year for surveillance.
On another front, it gives authorities the ability to hold aliens suspected of terrorist acts for seven days without filing charges, an increase from the current two days.
Mr Ashcroft had proposed there be no limitation on the length of detention in cases involving aliens suspected of terrorism. And he had proposed making it even easier for the government to conduct electronic surveillance to combat terrorism than the legislation would allow.
House negotiators also included, against Mr Ashcroft's wishes, a two-year sunset clause which means the new measures would expire at the end of December, 2003.
Mr James Sensenbrenner, the Republican chairman of the House Judiciary Committee from Wisconsin, and the panel's senior Democrat, Mr John Conyers, of Michigan, hoped to see push their proposal through the committee without hours and onto the floor of the House tomorrow. The Senate schedule is unlikely to complete its work on its version of the legislation until next week.
Meanwhile, USA Today reports that EU officials, due shortly to discuss streamlined extradition procedures with the US, are likely to require the US to guarantee that those handed over will not face the death penalty.
