Sen. Edward Kennedy, who earlier had said Law should remain in office, said his thoughts on Law's tenure should remain private. The charges against the church "are certainly the deepest wounds against the church in my lifetime," he said Wednesday.
Mayor Thomas Menino asked Boston residents to pray for Law, but wouldn't comment on whether he should remain.
"I pray for the cardinal also, but he'll have to make that decision, a decision that will be made by God and Rome," Menino said. "I can't get in the middle of that."
A poll released Thursday by Quinnipiac University found 60 percent of Massachusetts Catholics surveyed believe Law should resign because of his handling of sexual abuse cases involving priests; 27 percent said they didn't believe Law should resign; and 13 percent didn't know or didn't answer. The poll of 252 Catholics had a margin of error 6.2 percent.
Archdiocese spokeswoman Donna Morrissey said Thursday that no news conferences were planned.
The pressure on Law has increased since Monday when documents were made public detailing his handling of the Rev. Paul Shanley, accused in 26 complaints of molesting children.
Law, archbishop of Boston since 1984, moved Shanley from parish to parish and recommended him for a post at a California church without telling officials there of allegations in Shanley's past, according to the documents. Law's own advisers had called Shanley "a very sick person," and Shanley spoke approvingly of sex between men and boys, according to the documents.
The way Law handled the Shanley case was similar to the way he handled former priest and convicted child molester John Geoghan. Law has apologized for moving Geoghan from parish to parish despite allegations of pedophilia.
This week, two Democratic candidates for governor, Robert Reich and Warren Tolman, called for Law to step down, and The Boston Globe and The Union Leader of Manchester, N.H., joined the Boston Herald in calling for Law's resignation.
Law's supporters also have spoken out.
Ray Flynn, a former Boston mayor and ambassador to the Vatican, said Law should remain on the job to repair the damage suffered by the church.
"He's the one that's most in pain," Flynn said. "He's the one who has the most to lose. He will put his heart and soul into it."
Ralph DelVecchio, one of Geoghan's alleged victims, agreed that Law might be the best person to fix the problems, provided there isn't evidence he acted maliciously in shuttling priests between churches.
"I don't really believe he intentionally meant to be devious," DelVecchio said. "I think he could do more good staying there because he knows what's going on."