It's a tough sell, but not for the reasons you might think. Broadly speaking, House Republicans are on board; Democrats, not so much.
A major reason for the division is labor unions, which fear trade deals can take manufacturing jobs away from American workers and ship them overseas. Labor unions are also huge supporters of Democrats. So Obama and Republicans are in the odd situation of trying to convince Democrats to reluctantly give the president what he wants.
As they scramble to find the votes ahead of a potential vote on Friday, here are the six factions Congress falls into on trade.
1. The Labor Democrats
Who they are: Pretty much all House and Senate Democrats who don't want labor unions spending big money against them in their next campaigns. In the House, that's about two-thirds of the party's 180 Democrats. Labor unions have become the most vocal group on either side of the trade debate, and they appear to be putting their money where their mouth is. Politico reports labor activists say they'll run $84,000 in TV ads against a California Democrat who supports the fast-track bill.
On Capitol Hill, Rep. Rosa DeLauro of Connecticut and Sen. Elizabeth Warren of Massachusetts lead the charge for this group. On the campaign trail, Democratic presidential candidates Sen. Bernie Sanders (I-Vt.) and former Maryland governor Martin O'Malley also oppose the trade deals.
What they believe: That opening up U.S. markets to foreign countries will also open up American workers to lower wages and job losses, particularly while U.S. manufacturing companies take advantage of open borders to move plants overseas for cheaper labor.
There's some truth to that, economists say. By allowing goods and services to flow more freely across borders, trade deals helps countries specialize in just a few goods and services they're really good at. That makes economies more efficient but means some workers will inevitably lose out.
But the size of which industries like manufacturing will lose out in these trade deals is debatable, as many such low-wage jobs have already moved overseas.
Key talking point: Warren: The deals are "going to help the rich get richer and leave everyone else behind."
2. Silicon Valley Democrats
Who they are: A relatively small group of about 40 pro-business, moderate Democrats who are allied with Silicon Valley executives. The Washington Post's David Nakamura notes those executives include the influential Silicon Valley Leadership Group, which represents 390 companies, including Facebook, Google and Microsoft, and is aligned with tech CEOs from Cisco Systems, Oracle and AT&T in lobbying for fast track.
What they believe: That the trade deals -- and particularly Obama's massive 12-nation deal with Pacific Rim countries -- protects one of America's top money-makers: intellectual property. The deals as drafted strengthen patents and extend copyright protections for the things Americans are good at inventing, like pharmaceuticals, movies and technology start-ups.
This argument offers Democrats an alternative to labor unions' message: Perhaps some manufacturing jobs will indeed ship overseas, but low-wage manufacturing isn't where America's economy is headed anyways.
Key talking point: Obama made the best argument for this group recently: "If we are going to capture the future, then we’ve got to open up markets to the kinds of things that we’re really good at, that can’t be duplicated overseas."
3. On-the-fence Democrats
Who's in this camp: A handful of Democrats who are torn between supporting their president and the labor unions' strong pull. These Democrats include House Minority Leader Nancy Pelosi of California and Minority Whip Steny H. Hoyer of Maryland. This group is small but significant; Obama and Republicans need about 25 Democrats to support the fast-track legislation when it comes to a vote, so the president is lobbying these people hard.
What they think: Two competing thoughts here: Let's give our president what he wants … but I don't know if that's worth risking a primary challenge supported by labor unions.
With the vote count coming down to the wire, the AP's Josh Lederman reports Obama has promised to help campaign in 2016 for anyone in this group who crosses the line and votes yes for fast-track legislation.
Key talking point: "There’s a difference between growing the economy and helping American companies grow the bottom line and creating jobs." Rep. G.K. Butterfield (D-N.C.) told The Hill.
4. Gung-ho trade supporters
Who's in this camp: Establishment Republicans, including leaders like House Speaker John A. Boehner (Ohio) and Senate Majority Leader Mitch McConnell (Ky.), have Obama's back on fast-track legislation and the two trade bills. In the House, they have the support of about 110 Republicans, according to The Hill's whip count.
What they believe: Trade deals are job creators, because they allow the United States to require other countries to the same labor and environmental standards that our businesses must follow. That makes a more even global playing field for Americans. And fast-tracking the deals is the only way to get them negotiated; imagine if every country involved allowed its legislative bodies to chime in. Nothing would get done!
Key talking point: "We have a chance here to write the rules on our terms," said Rep. Paul Ryan, a Wisconsin Republican who is central to crafting the fast-track legislation. "We have a chance here to write the rules on our terms, to raise other countries to our standards, to create more opportunity for our people."
5. The anti-Obama Republicans
Who's in this camp: Republicans who might support fast-track legislation and the trade deals but who are wary of giving the president so much authority to negotiate them without Congress's input. This camp encompasses about 50 of Republicans' Southern and tea party-leaning lawmakers.
What they believe: By voting for fast-track legislation, they're essentially blocking themselves from the discussion about what should be put in the trade deals.
Key talking point: Here's one from Alabama Rep. Bradley Byrne's (R) office: "Congressman Byrne is a strong supporter of free trade, which supports almost 3,000 jobs in the 1st district alone. That said, he believes Congress must have a seat at the table as the trade negotiations continue."
6. The swing-state Republicans
Who's in this camp: About 12-20 recently elected House Republicans who came into power during midterm Republican waves and now represent swing districts with decisive moderate constituents who might not like Obama's trade deals. They include Midwestern lawmakers like Ohio's David Joyce and Long Island's Rep. Lee Zeldin.
The environmentalist group Sierra Club recently held a rally in Zeldin's district to convince him to oppose the fast-track legislation.
What they believe: This group usually aligns with the Republican establishment on most issues. But on trade, these lawmakers carry the same concerns as Labor Democrats: A vote for fast track could mean a vote for them out of office.
Key talking point: "I support trade," Zeldin told Facebook supporters in March. But on the trade deals and fast-track authority, "I will read it and decide at that time whether to vote for it or against it."