"I can confirm that the deadline is this evening, at the end of the business day," a spokesman for Swiss financial market regulator FINMA, told AFP, refusing to say how many banks had already signed up to take part in the programme.
Washington alleges that Swiss banks have helped US citizens hide billions of dollars in assets from tax authorities, in a row that has soured ties between the two in recent years.
Under a deal recently reached between Bern and Washington to end the dispute, Swiss banks can avoid US prosecution by voluntarily handing over information on American clients, as well as by paying a fine.
The penalty would be equivalent to between 20 and 50 percent of the value of undeclared accounts, depending on when they were opened.
Banks that opened undeclared accounts for US clients before 2009, when Washington fined Switzerland's biggest bank, UBS, $780 million for complicity in tax evasion, will face lower penalties.
But the penalties would be higher for those that accepted undeclared assets from US clients after that, according to the agreement.
Banks that do not take part in the disclosure programme also risk far stiffer penalties and prosecution in the United States if Washington discovers that they have indeed helped Americans hide assets.
Swiss Finance Minister Eveline Widmer-Schlumpf, who negotiated the deal with Washington, made a last-minute appeal on Monday to the banks, urging them to join the programme.
Swiss experts, meanwhile, disagree on how the banks should act.
Geneva University law professor Xavier Oberson said the banks would be better off falling into line, while business lawyer Douglas Hornung advised against that in a recent opinion piece in the Le Temps daily.
"If the United States is threatening all the Swiss banks that it will block their access to the US market and to conducting operations in dollars, let it say so clearly, and let Switzerland take the country before . . . the World Trade Organization for abusing its dominant position," Hornung wrote.
"But please, don't give in to inexcusable blackmail and let us remain the proud masters of our destiny, and of our past," he said.
"We have a choice."
A major tax case launched by US authorities against Switzerland's oldest bank Wegelin & Co. forced the institution to close.
The bank, which was founded in 1741, pleaded guilty to helping Americans hide funds in secret accounts.
It was fined a total of $57.8 million for helping wealthy individuals avoid at least $20 million in taxes.
The deal with US authorities pierces the tradition of secrecy upon which the Swiss banking industry was built, and the country has also signed up to international agreements that threaten to weaken it further.