"If she does not resign, then the House will move ahead with impeachment preparations," said Speaker Sam Smith (R., Jefferson).
Melvin, a Republican from a prominent Western Pennsylvania family, rebuffed earlier calls for her resignation.
"Maybe she sees the light of day and resigns," said a Democratic legislative aide. "People are not expecting that to happen."
If she does not step down, there are several ways she could be removed.
She could be impeached by the state House and then tried and convicted in the Senate. Melvin would have no recourse in that event.
When she is sentenced by Allegheny County Court Judge Lester G. Nahaus, he might order her removed from office.
That's what happened in 1994 to Rolf Larsen, the last Pennsylvania justice to be convicted of a crime while in office.
Larsen appealed the judge's order, however, and the legislature moved forward with impeachment.
Impeachment could embroil Harrisburg for months in an embarrassing spectacle. The Larsen impeachment resolution was introduced in May 1994. The Senate convicted him in October.
Also, a pending case against Melvin in the Court of Judicial Discipline, which was put on hold during the criminal trial, is proceeding.
She has 30 days from her conviction to file legal arguments before the court, which has the authority to remove her.
Melvin could ask for a special tribunal to review any removal order by the court, but it would be limited in scope, said Lynn A. Marks, executive director of Pennsylvanians for Modern Courts.
Marks was a leading advocate for the 1993 constitutional amendment that created the Court of Judicial Discipline, and said Melvin's conviction should spur another constitutional amendment - for merit selection.
Contact Robert Moran at 215-854-5983, firstname.lastname@example.org.
Inquirer staff writers Amy Worden and Angela Couloumbis contributed.