Japan has two difficult options as it continues trade discussions with the United States: Get slapped with auto tariffs or make concessions that could hurt Prime Minister Shinzo Abe's support at home.

Bilateral talks between the U.S. and Japan are currently underway in Washington. The administration of President Donald Trump has the upper hand as it's "wielding the threat of automobile tariffs pretty effectively," said Tobias Harris, vice president at Teneo Intelligence.

Car exports to the U.S. are a key source of growth for Japan, accounting for around 1 percent of the country's gross domestic product, according to trade statistics from both countries. The U.S. has said it's considering imposing tariffs of up to 25 percent on auto imports, which would hurt demand for Japanese cars.

"I think Japan now finds itself in a position where it has to choose between accepting those tariffs — which I think are unacceptable — and possibly making concessions in the areas that could be politically difficult for Abe. So they're going to a find a way to thread the needle between those two unpleasant options," Harris told CNBC's "Squawk Box" on Friday.

Abe is heading into a leadership contest within his own party next month. Winning the race in the Liberal Democratic Party would place him on track for a third three-year term in power.

Japan's upper house of parliament is also due for elections next year and making too many concessions with the U.S. may hurt his political support base, analysts said.

Abe could offer the U.S. greater access to its agricultural sector to avoid tariffs on its automakers, some observers say. Tokyo had previously done so when it entered a multilateral trade pact — the Trans-Pacific Partnership — with the U.S. which eventually pulled out of it.

But making the same offer in a bilateral setting may be tough for Abe as Japan could be seen as giving in to the U.S., analysts said.

"Let's remember where Prime Minister Abe comes from: He's a conservative, he's a hawk, he comes from the right of the LDP and that traditional power base has been the farmers," Andrew Staples, global editorial director and Southeast Asia director at The Economist Corporate Network, told CNBC's "Street Signs" on Friday.