Hawaii state House Democrats will meet this week to gauge whether they can come up with the votes to pass a bill legalizing same-sex marriage.

If there is sufficient support, and if legislative leaders can agree on language that would withstand court challenges, Gov. Neil Abercrombie (D) will call a special session to deal with the issue this fall. Abercrombie told the Honolulu Star-Advertiser he thinks it’s “very likely” there will be a special session.

“I think we can put together something that can achieve a solid majority, that will give us the opportunity to establish marriage equity in the state of Hawaii commensurate with the recent Supreme Court decisions, and will satisfy and resolve the issues that are presently before the appeals court on the mainland,” Abercrombie told a gathering of state Democrats.

Abercrombie’s chief of staff, Blake Oshiro, is working on language with the state attorney general’s office, the Star-Advertiser reported Monday. State Senate leadership says they have the votes to pass a same-sex marriage bill.

Democrats have overwhelming majorities in both legislative chambers; they control the House by a 44-7 margin, and they hold 24 of 25 seats in the Senate. But the legislature has to rely on Abercrombie to call a special session because they can’t meet the two-thirds threshold to call one themselves.

Hawaii passed a constitutional amendment giving the legislature power to define marriage as a heterosexual union in 1998, but the legislature partially reversed itself in 2011, legalizing civil unions between same-sex couples.