Beacon Hill's been holding its breath for weeks looking forward to finding out whether the Legislature would force Gov. Charlie Baker's hand on whether to codify public access rights for transgender people. But Baker may have come to the rescue of skittish House Democrats Tuesday, when he announced that he would sign into law that chamber's version of the bill.

The House is set to vote Wednesday on a long-awaited bill that would include transgender men and women in antidiscrimination laws when it comes to restaurants, public bathrooms and changing areas.

"After hearing from all sides and carefully reviewing the two separate proposals that have been working their way through the legislature, I believe the House version addresses the concerns that some have with the bill by requiring the Attorney General to issue regulations to protect against people abusing the law. I would sign the House version in its current form should it reach my desk," Baker said in a statement from his spokeswoman Tuesday afternoon.

Baker's move essentially lets the House off the hook on having to deliver the two-thirds vote margin necessary to override the governor's objections. Without the spectre of a veto threat from Baker, DeLeo is free to let his more conservative members vote their conscience and pass the bill with a simple majority.

"I generally sense a sense of approval for the legislation, DeLeo told reporters after caucusing with his Democratic members Tuesday afternoon.

When asked if he thought the body would come up with a veto-proof majority to override an attempt by Baker to reject the bill, DeLoe was less certain.

"I'm not so sure about that. I do feel we will have the votes to pass but whether it's veto proof, I'm not so sure," DeLeo said.

Baker previously told the Boston Globe of his intention to support the House legislation.

Even before Baker's announcement, DeLeo insisted that for the Legislature to have any hope of getting transgender accommodations into law, the Senate would have to go along with the House bill, which includes language to lay out additional punishment for those who abuse accommodations access in order to commit crimes. The Senate easily passed their version of the bill without additional provisions earlier this month.

"It is my hope that at the end of the day, senators - and they have their strong beliefs as well - will realize that if we're going to make this a reality, then the House bill is going to be the way to go," DeLeo said. 

"I'm not looking to get up there tomorrow and to pass a piece of legislation, feel good about it, say "ra ra, look what we've done' and not have it passed into the law. That's not what I'm all about," The Speaker, who has been at odds with Senate leadership over procedural issues, added.

Though the bill is now much closer to passage in one form or another, some Republicans and conservative-leaning Democrats still resist the additional anti-discrimination legislation and fear it may lessen public safety for adults and children.

Rep. Keiko Orral (R-Lakeville) thinks the law as it stands already includes transgender people and says she's inclined to vote no. 

"They're not necessarily concerned about transgender people and where they go to the bathroom. It's more the locker rooms and the showers where people are fully disrobed and feeling very vulnerable," Orrall told WGBh News.

Orrall offered an amendment to the bill that would clarify religious exemptions for access, which she said is an issue lawmakers need to debate.

"We need to understand, does this apply to a mosque? Does this apply to a synagogue, an orthodox synagogue? Does this apply to our churches?" Orral said.