One of the amendments from Sen. Orrin Hatch (R-Utah) would ensure that TAA, which is designed to help American workers hurt by international trade, only resumes if the Congress and the president pass pending free-trade agreements with Colombia, Panama and South Korea.
Some Democrats are demanding a vote on TAA as a precondition for taking up those agreements.
The second amendment, from Sen. John McCain (R-Ariz.), would extend TAA through 2014 as part of the GSP bill.
The Senate is set to reconvene at 9:30 a.m. Wednesday, and vote on these amendments.
This story was updated on Wednesday at 3:07 p.m. to reflect that those votes occurred on Wednesday, not Thursday.