Gay Rights Gaining Momentum
The special session was originally expected to last five days, but there is already talk of the legislature taking two weeks to complete its work.
Abercrombie, who served more than two decades in the US House of Representatives before running for governor in 2010, signed a same-sex civil unions bill into law two years ago and has since been a vocal proponent of gay marriage.
His immediate predecessor, Republican Linda Lingle, vetoed a civil unions bill in 2010.
Just one year ago, only six states and the District of Columbia recognized same-sex marriage. That number has more than doubled since then, due in most cases to litigation over the issue.
Maine, Maryland and Washington state became the first three states to extend marriage rights to same-sex couples by popular vote with passage of ballot initiatives last November.
In June, the US Supreme Court forced the federal government to recognize same-sex marriages performed in states where such unions are legal and upheld a lower-court decision throwing out a state ban on gay matrimony in California.
And last week New Jersey Governor Chris Christie dropped his legal opposition to gay marriage, making his state the 14th to legalize same-sex weddings.
The New Mexico Supreme Court is expected to decide by year's end whether same-sex marriage should be recognized statewide rather than county by county, and the Illinois legislature is also considering the issue.