“Abe will work on convincing Trump that continued corporate cooperation will promise greater employment opportunities for Americans in the U.S.,” said Shawlin Chaw, a senior analyst at Control Risks, a global risk consultancy.

“There’s a lot of uncertainty in U.S.-Japan relations right now. Abe wants to ensure a sound footing for the future of bilateral relations to see how much he can push and prod the U.S. for something larger,” she said.

There’s another reason a bilateral deal may be tough: History.

Terada Takashi, a visiting professor specializing in international relations at National University of Singapore, said that in the 1980s and 1990s, Japan made a lot of concessions to the U.S., while the U.S. ignored many of Japan’s requests, creating a “poor” relationship.

The difficulties of negotiating a trade deal with a much-larger partner may have spurred some of Japan’s enthusiasm for TPP.

“In a multilateral [deal], smaller nations can create a bloc to negotiate,” countering “powerful leverage,” noted Takashi.

Trump’s walking away from TPP also damaged at least some of Abe’s structural reform drives, which may sour the outlook for a bilateral deal.

“There will be an impact on Abe’s ability to push through some reforms,” particularly in the agriculture and health care sectors, Control Risks’ Chaw said. “Without the promise of a bigger export market, it’s more difficult.”

One example is that Abe’s administration managed to push through some liberalizing measures for the tightly controlled agriculture sector with the promise of more to come to comply with TPP, in part by dangling the prospect of access to large export markets such as the U.S.

Reforming the agriculture sector has long been politically unpalatable in Japan, even though it’s widely believed to be necessary in a country where food prices are considered relatively high because of the segment’s inefficiencies.

Without reform, agriculture in Japan may become even more inefficient.

Outside of Hokkaido, the majority of farms are less than 3 hectares (7.4 acres) in size, with the average size less than 1 ha, according to data cited in a 2009 OECD report. In Hokkaido, the average farm size is still only 16.45 ha (40.6 acres), the data show.

Government data indicate that the average age of the nation’s farmers is over 66 years, with many lacking successors.

But without TPP, further liberalization may be off the table, and Japan media have reported recently that Abe said that even in a bilateral deal, Japan would protect key agricultural products, such as rice, beef and wheat.

“Probably, Japanese farmers are not necessarily so much encouraging the more liberalized movement,” noted Terada Takashi, a visiting professor specializing in international relations at National University of Singapore.

Takashi noted that without TPP, Australian and American rice farmers will likely now need to pay higher tariffs to access the Japanese market.

That was also noted by other analysts.

“It’s difficult for Japan to open the agriculture market without reciprocity from the U.S. on other sectors,” Control Risks’ Chaw said. “U.S. agriculture companies will face resistance and limitations.”

—By CNBC.Com’s Leslie Shaffer; Follow her on Twitter @LeslieShaffer1

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