What do Obama (and Republicans) want?
The White House does not strictly need TPA in order to pass the trade bill, but administration officials told CNBC that such a situation would allow for more power at the international bargaining table. The argument goes that any deal could be mangled on Capitol Hill without TPA, so potential partners would feel less confident in U.S. capacity to deliver on any agreements.
The proposed Pacific trade agreement itself, known as the Trans-Pacific Partnership (TPP), was already nearing the final stages of negotiation in March, an administration official told CNBC at the time. Those discussions involve 11 countries besides the United States—Australia, Brunei, Canada, Chile, Japan, Malaysia, Mexico, New Zealand, Peru, Singapore and Vietnam.
Read MoreMajor Asia-Pacific trade pact enters final stages
The White House and many lawmakers argue that this agreement is crucial to proving that the U.S. "pivot" to Asia is not just a shift of military assets, but also an economic commitment to the region. They also argue that it will open up markets to American exports, thereby strengthening the U.S. economy.
Some politicians say the TPP is necessary to fight China's influence in the area, establishing an American-led system of regional trade standards, though the White House publicly dismisses that position.
Rep. Paul Ryan made that claim in an interview with CNBC's "Closing Bell" in April.
Read MoreJapan's Abe to Congress: TPP's value is 'awesome'
"China is going around the world trying to write the rules for the global economy to benefit themselves," the former Republican vice presidential candidate and chairman of the House Ways and Means Committee said. "I don't think that's in our interest. ... We're either helping shape the global economy, or it's shaping us."
—Reuters contributed to this report.