Sen. Jeff Sessions is the most outspoken Republican critic of President Obama's trade agenda, warning that it will harm American jobs and wages as well as give the White House further power to bypass Congress while setting immigration policy.

"Members of Congress have a choice: they can either put blind faith in the verbal assurances of the Obama administration — that this time is different — or they can demand that we slow down, read the fine print, and not fast-track anything unless we can be sure it will increase, not reduce, jobs and wages," the Alabama Republican said Monday.

Yet in a crucial Senate vote Tuesday on Trade Promotion Authority legislation, also known as "Fast Track," a key part of Obama's agenda, Sessions was one of 52 lawmakers who voted with the administration to allow debate to proceed on the bill. All Democrats except one opposed it, stalling the legislation and badly damaging its chances for passage. No Republicans voted against it, except Senate Majority Leader Mitch McConnell, R-Ky., in a procedural move that will allow him to revive the bill later on.

The situation shows why Obama's trade agenda may be in even worse shape than Tuesday's 52-45 loss would indicate. The number of Senate opponents may grow larger from this point forward as Republican critics join in. Their votes Tuesday allowing debate do not mean they will back ending debate later on.

That's the argument Session's office made, noting that Tuesday's vote was a "motion to proceed" to begin debating the legislation. A second, final, cloture vote would likely have been needed to end debate.

"It would be a significant mistake to interpret Democrat or Republican votes on the motion to proceed in terms of where those members will fall on supporting or opposing final cloture on the bill," a source said.

In an email to reporters at about the same time as the vote, Sessions' office warned that supporting Fast Track would virtually assure that any trade deal the White House presents to Congress would pass.

"Every fast-tracked trade agreement has been subsequently adopted. There is no history of Congress ever enforcing violations of the 'negotiation principles' (which are not binding) by rejecting an unamendable deal," the email warned.

Another Republican critic, Sen. Rand Paul, R-Ky., also voted to proceed despite having come out publicly against renewing Fast Track legislation as recently as Monday. "I've told leadership I'm a 'no' vote on Trade Promotion Authority," the presidential candidate told New Hampshire radio station WMUR. "I'm hesitant to give blanket authority on stuff we haven't seen." Paul's office did not respond to a request for comment.

Fast Track legislation would prohibit Congress from amending trade deals, limiting lawmakers to a strict up or down vote. The bill is widely seen as crucial to the rest of Obama's agenda, especially the Trans-Pacific Partnership, a major 12-nation trade bill.

The bill has scrambled the usual partisan lines. Senate Majority Leader Mitch McConnell, R-Ky., is backing the White House, while Democrats have objected. Tuesday's vote was well short of the 60 needed to proceed.

Democrats argued that the Senate needed to consider amending the bill to include trade protection and currency manipulation provisions. Sen. Orrin Hatch, R-Ore., a co-author, said they were being disingenuous.

"This demand materialized last week and came from the Senate Democratic leadership, virtually all of whom oppose TPA and their president outright," Hatch said Tuesday.