BOSTON (AP) – Gov. Deval Patrick became the first sitting governor to march in the city’s Pride parade Saturday, just days before state lawmakers are expected to vote on a ballot question that could ban same-sex marriage.

The Democrat, who walked with his daughter, Katherine, and Mayor Thomas Menino in the 37th annual parade, said he wanted to keep Massachusetts a state where same-sex couples could marry legally.

Patrick said the 2003 court decision that paved the way for same-sex marriage “affirmed the principle that everyone comes before the court as equals.”

“That is an argument we need to make to representatives and senators this week,” he said. “What experience has taught us is that the sky hasn’t opened up, families are still intact.”

Patrick said he’ll ask lawmakers to postpone this week’s scheduled vote on a proposed constitutional amendment barring same-sex marriage if he doesn’t think there are enough votes to kill the measure.

“We want a vote that goes the right way, that keeps us off the ballot,” Patrick said Thursday after attending an evening fund-raiser for MassEquality, an advocacy group that opposes the amendment. “If we need more time, we’ll ask for more time.”

Patrick, who supports the 2003 Massachusetts Supreme Judicial Court’s decision barring the state from denying marriage licenses to same-sex couples, said he’s been on the phone trying to round up enough votes to defeat the measure. He wouldn’t say if he’s received any commitments from lawmakers agreeing to change their position.

Both sides agree that 57 lawmakers have either voted in favor of the question in the past or pledged to support it.

Opponents need to convince eight of those lawmakers to change their minds to block the question from reaching voters on the 2008 ballot. Supporters of the amendment need to hold on to at least 50 state lawmakers.

Patrick, who said he wants a vote on the merits of the amendment, said he didn’t underestimate the strength of the supporters of the question.

“There are still great passions and great fear and great intolerance on the other side,” he said.

Supporters of the question say their coalition of lawmakers is holding firm. They also urged legislative leaders to allow a vote when House and Senate lawmakers meet in a joint constitutional convention this week.

“We have had no indication of any of our 57 legislators changing their vote,” said Kris Mineau, president of the Massachusetts Family Institute. “Most of the representatives I’ve talked to are feeling tremendous pressure, but they’re standing firm.”

He added: “There’s a lot of arm-twisting going on.”

The final decision about whether to call for a vote next week rests with Senate President Therese Murray, D-Plymouth. As senate president, Murray – a supporter of same-sex marriage – presides over the constitutional convention.

Her spokesperson, Ann Dufresne, said Thursday that Murray wants a vote, but also wants to defeat the measure.

“She is going to convene the [constitutional convention] on Thursday, but whether we get to the same-sex marriage question is really dependent on the members,” Dufresne said.

If Murray isn’t convinced there are enough votes to kill the amendment, she could recognize a motion to postpone the constitutional convention to another date to give opponents of the measure more time to change votes.

Same-sex marriage activists remained upbeat about the chances of changing the eight votes needed to block the question from reaching the ballot.

They point out that for the first time all three of the top political leaders on Beacon Hill – Patrick, Murray and House Speaker Salvatore DiMasi, D-Boston – support same-sex marriage. Last year, former Gov. Mitt Romney and former Senate President Robert Travaglini opposed same-sex marriage.

In 2003, the Supreme Judicial Court barred the state from denying marriage licenses to same-sex couples. But it also ruled last year that lawmakers must vote on the proposed ballot question, instead of letting it die without a vote, as some lawmakers advocated.

As the constitutional convention approaches, both sides have been increasing pressure, stalking Statehouse halls and appealing directly to voters.

MassEquality campaign director Marc Solomon said the group has spent $750,000 on a media campaign on television, print and Internet ads, and a direct mail appeal. Supporters of the question have also taken to the airwaves.

If the ballot question receives support from 50 of 200 state lawmakers at a Constitutional Convention scheduled for June 14, it would be placed on the 2008 ballot.