The move approved on Monday will allow Washington to obtain details of tax cheats from Swiss banks with greater ease.
"I hope we can get something that satisfies both parties," Beyer told the Swiss German-language evening news programme, Tagesschau, noting that many issues still need to be ironed out.
"This is a positive and useful step forward for the United States and Switzerland together," said Beyer.
The new treaty would allow US authorities to demand information on suspected tax cheats, even without identifying the suspects' names or addresses, if the bank in question or its employers have acted illegally.
If no illegal action has been associated with the bank or its employees, then it would remain necessary for Washington to identify the suspect in order to obtain help from Switzerland to release the person's details.
Parliament passed the treaty while Bern and Washington are in negotiations over 11 Swiss banks which the US has accused of helping US taxpayers hide assets.
The tax probe had led to the collapse of Wegelin, Switzerland's oldest private bank. Three of its bankers have been charged with conspiring to help American clients hide funds.