McCain also noted that the Obama administration has proposed ending this program.
Sen. Bob Casey (D-Pa.) argued after McCain spoke that he will oppose his amendment if it comes to a vote. McCain's amendment would be to H.R. 2112, a "minibus" appropriations bill that the Senate could pass this week.
The TAA program was reauthorized by Congress last week as part of an agreement that also allowed Congress to approve free-trade agreements with Colombia, Panama and South Korea.
The White House on Tuesday announced that President Obama will sign the FTAs this Friday in the Oval Office, and then make remarks about them in the Rose Garden along with industry and labor leaders.
Once the bills are signed, the trade agreements are expected to take effect sometime early next year.