In addition to the traditional arguments for trade deals, administration officials and many Republicans contend that the so-called Trans-Pacific Partnership would help underscore the U.S. pivot toward Asia—and establish Washington's system in a part of the world increasingly influenced by Chinese interests.
Read MoreSenators rake in big money from pro-trade donors
TPA means that the White House can present its finalized trade deals to Congress, and the legislature is only given the option of voting for or against the agreement—not amending the terms.
Most trade experts interviewed by CNBC say that would-be trade partners are unwilling to sign onto an agreement if the president isn't given fast track status: They fear that Congress would otherwise disassemble any hard-fought terms. Administration officials, however, have said they would not be wholly stymied if TPA fails.
The TPP, potentially a legacy-defining achievement for Obama, would be the biggest free trade agreement in a generation. It would cover 40 percent of the world economy and raise annual global economic output by nearly $300 billion.
Negotiators say a deal on the TPP, which would open new markets for U.S. exporters such as Caterpillar and Microsoft, could be wrapped up within weeks once countries are sure U.S. lawmakers will not pick the deal apart afterward.
—Reuters and The Associated Press contributed to this report.