“Nothing I’ve been involved in during my years in politics has ever been as excruciatingly painful as the fight over this bill,” said Assemblyman Charles D. Lavine, a Long Island Democrat who is among two dozen lawmakers who supported the Markey bill in past years, but hesitated this year.

Mr. Lavine changed his mind after priests and residents in his predominantly Italian-American and Hispanic district, especially older voters, started swamping his office with phone calls last winter, expressing their opposition. The pressure, which went on for months, led him to consider  for the first time, he said  the “humongous financial burden and, frankly, the ridicule” that the Child Victims Act and resulting lawsuits would inflict on the church.

His yes votes in past sessions, he said, were made partly with the knowledge that the Republican majority leader in the Senate, Joseph L. Bruno, a staunch opponent, would never let the bill see daylight in that chamber. Mr. Bruno stepped down in 2008.

“When it was never going to fly anyway, there was a tendency for many of us who are concerned about victims’ rights to symbolically support legislation like this,” Mr. Lavine said.

In the same way, the Catholic hierarchy in New York never felt it had to mount a serious campaign against the bill as long as Mr. Bruno held the line, according to lobbyists and legislative aides. Their effort this year forced longtime backers of the bill, like Mr. Lavine, to weigh the potential consequences of that support against their empathy for abuse victims.

With 76 votes needed for a majority in the 150-member Assembly, Ms. Markey’s bill passed with close to 100 votes in past years. This year, the bill’s solid support ranged, depending on the day, between 70 and 80, Ms. Markey’s aides said.

Lobbyists and advocates on both sides say other factors contributed to the change in climate.

When the Democratic Party leadership in the Senate was toppled on June 8 by the defection of two members to the Republican ranks, wavering supporters lost an incentive to risk the church’s ire in the crucial final weeks of the Assembly session.