They argue that Vietnam is selling its exports at unfairly low prices, driving American firms out of business and losing tens of thousands of jobs.
Nonetheless the failure to pass the bill at the initial stage came as a surprise to many business lobbyists.
The bill had received strong backing from many US business leaders, keen to gain a foothold in Vietnam - one of South-East Asia's fastest-growing economies and soon to become the latest member of the World Trade Organisation.
Supporters of the bill are expected to try again on Wednesday to secure its passage through the House of Representatives.
This time it will need only a simple majority, rather than the two-thirds majority needed on Monday as Republicans sought to push the bill through with limited debate.
Trade between the US and Vietnam has grown quickly since a bilateral trade deal signed in 2000.
But American businesses will not be able to take full advantage of Vietnam’s accession to the WTO unless it passes the trade normalisation bill first.
The Bush administration has given strong backing to the bill, and the president had been hoping to see it passed before he arrives in Hanoi later this week.
In a separate development before Bush's visit, the White House said on Monday that it had removed Vietnam from a list of countries considered to be the worst violators of religious freedom.
Welcoming the announcement, Ngo Yen Thi, head of Vietnam’s Religious Affairs Commission, said the US decision was "in line with warmer relations between the two countries".