The approval will hinge on support from "strong pro-trade Democrats" and Republicans "who historically, at least, have been in favor of the free market," Obama said at a meeting of American governors at the White House.
"I am cautiously optimistic that we can still get it done," he said.
Once the trade deal is in place, "American companies and American workers will be better off than the existing trade regime that we have right now," Obama said.
The ambitious Trans Pacific Partnership (TPP) would slash tariffs and trade barriers for an enormous 40 percent of the global economy and establish the largest free trade area in the world.
Its aim, in part, is to wrest influence from a booming China.
The deal must now be ratified by the 12 participating countries and the United States, where the Congress is deeply divided.
A number of Democrats are opposed, including Hillary Clinton and Bernie Sanders, the two candidates vying to be the party's nominee for the White House.
Republicans, who hold a majority in Congress and generally support free trade, have been mixed in their response.
Beyond objections to points in the deal itself, many are reluctant to give Obama a final political victory before he leaves the White House in January 2017.
The leader of the Republican majority in the Senate, Mitch McConnell, has warned that the deal would not garner the votes needed if presented for ratification before presidential elections in November.
The 12 signatories to the TPP agreement are: Australia, Brunei, Canada, Chile, Japan, Malaysia, Mexico, New Zealand, Peru, Singapore, the United States and Vietnam.
Source: The peninsula Qatar