The ruling Liberal Democratic Party is stuck between a rock and a hard place over whether to raise the threshold for tax exemptions from the current ¥1.03 million ($6,740) — which, if implemented, could rally much-needed support from the opposition Democratic Party for the People, but would slash tax revenues.

The LDP and the DPP’s policy chiefs officially kicked off discussions Friday on policies they could potentially agree on, with the key item being the latter’s proposal of raising the exemption threshold for income and resident tax to ¥1.78 million.

DPP’s support would be crucial since the LDP and its junior coalition partner, Komeito, no longer have a majority in the powerful Lower House after their defeat in last month’s general election.