Under the New York Constitution, the state Legislature has the power to fill the vacancy for the attorney general's job with a temporary appointment until Schneiderman's term expires at the end of the year.
Cuomo, who's running for a third term, has said he has his own favorites for consideration, among them his staff counsel, Alphonso David.
Underwood, the former US solicitor general, is one of 13 candidates who will interview with the state Legislature beginning Tuesday afternoon in hopes of filling out the final seven months of Schneiderman's term.
Orange County Legislator Jim O'Donnell is the Republican candidate for the 18th District House seat.
Candidate interviews will continue through Tuesday night and again on Wednesday.
"I think it's an understatement to say that none of us expected to be sitting here today for this objective", Underwood told senators and Assembly members gathered Tuesday at a meeting room in the state Capitol complex. "We want to interview her and every other person". "I've argued 20 cases in the U.S. Supreme Court, 21 cases before our state's highest court, and 33 cases in the Second Circuit - and I've closely supervised the work of other attorneys on hundreds more".
Yassky offered his support for Underwood on Twitter on Monday, describing her as "a superlative public servant and is uniquely equipped to serve as attorney general at this juncture". "But I can assure you that's not who I am".
He told lawmakers it "would not be a bad decision" if they were to keep Underwood in the interim role.
"I'm not sleeping very much", she said with a laugh. Several candidates who chose not to go through the Legislature's appointment process are expected to compete for their party's nomination to run for attorney general.
Thomas Abinanti, the next applicant whom the committee considered Tuesday, joked that the room had already cleared out, and that the state "could do a lot worse" than Underwood. Zephyr Teachout, who created an exploratory committee this week; and state Sen.
On Tuesday, James opened a campaign account for a potential run for attorney general.
She said some people joke that the National Association of Attorneys General is actually the "National Association of Aspiring Governors".