The Massachusetts House last week quietly set aside a budget amendment requiring Republican Gov. Charlie Baker to appoint a Democrat to serve as interim senator should Sen. Elizabeth Warren leave office, but it appears that the idea still is alive.

One top House leader said after Thursday's late-night budget session that the timing just might not have been right.

"I think it's a little early to get in front of that at the moment," House Ways and Means Committee Chairman Rep. Aaron Michlewitz told three reporters at the Statehouse, after the House approved its $46 billion fiscal 2021 budget.

Since her 2018 reelection, Warren has run for president, was in the mix for vice president, and now is mentioned as a Treasury secretary option in the developing administration of President-elect Joe Biden.

Michlewitz said House leaders didn't feel it necessary to pass the proposal as a budget amendment, but hardly ruled out the idea.

"I know that there's a lot of speculation going on about potential maneuvers that could take place," he said. "I think it's a conversation that we are all willing to have at some point in time."

Baker said last week that he would veto a change to the appointment law, but Democrats have the numbers to override a veto if they stick together.

The proposal "may be better for another day," Michlewitz said, citing the urgency around getting a final fiscal 2021 budget to Baker as soon as possible.

If Biden taps Warren for Treasury or any other post, that day could be soon, as assembling a Cabinet is among the top priorities of any president-elect.

The pick for Treasury is being watched closely, because of that appointee's role in forging economic, tax and business regulation policies.

In a report Friday, Warren didn't make The Washington Post's list of three possible Treasury appointees. The Post named as options former Federal Reserve Governor Lael Brainard, former Federal Reserve Vice Chair Roger Ferguson, and former Federal Reserve Chair Janet Yellen.

The New York Times last week had Warren on its list, along with Brainard, Yellen, former Deputy Treasury Secretary Sarah Bloom Raskin and Atlanta Federal Reserve President Raphael Bostic.

The House and Senate in July voted to change legislative rules and extend formal sessions through 2020, which means lawmakers can address the appointment proposal, if leaders wish to, without being concerned about Republicans blocking it during informal sessions, which are customary during the lame-duck period.

A Warren departure would trigger a wide-open scramble for her Senate seat, with a Baker appointee holding the job down on an interim basis until voters weigh in during a special election that likely would be held in the spring.

If the Legislature were to change the rules, it would be the third Senate vacancy rule change since 2004, when the Democrats on Beacon Hill acted to strip then-Gov. Mitt Romney of his appointment powers when they thought John Kerry might win the White House.

The current law allows the governor to make a temporary appointment to fill a vacant seat in the U.S. Senate until a special election can be held within 145 to 160 days of the vacancy. It previously was changed in 2009, at the request of U.S. Sen. Edward Kennedy, who was ailing and concerned about securing the votes needed to pass the Affordable Care Act.

"It's a bad look for everybody, and if they were to send legislation to change the rules yet again, you know, and I don't say this very often, I'd veto that because I think situational dynamics around this stuff when it comes to process associated with elections, it's just a bad look for government generally," Baker told WBZ-TV's Jon Keller on Thursday.

The balance of power in the U.S. Senate is riding on two Senate elections in Georgia, with Democrats needing to win both to gain a narrow edge. An appointment law requiring Baker to name a Democrat would limit his choices, but also remove any opportunity for him to help national Republicans by naming a GOP senator.

Another top state officeholder in Massachusetts also was the subject of some speculation about her future last week. In an interview on Boston Public Radio, Suffolk County District Attorney Rachael Rollins said Attorney General Maura Healey was in the mix for a U.S. Justice Department post.

Asked about her favorites for U.S. attorney general, Rollins said, "I am hearing that our very own attorney general of the Commonwealth of Massachusetts is on a short list as well." Rollins went on to discuss the importance of the Office of Civil Rights in the Department of Justice.