"It's very important we try to minimize the disruption," said Boggs, who anticipates the selection of a new speaker will be "fair, friendly and equitable."
Miley, who had been contemplating a run for state Senate in 2014, said he is now considering seeking the speaker's post.
He had not made a final decision as of Thursday. "To some degree or another, I'm sure all delegates are interested in being speaker," he said.
Both Miley and White, who could not be reached for comment, have to make a decision on whether to risk their chairmanships on a run for speaker, or instead try to solidify their current positions by throwing their support to the new speaker.
House Minority Leader Tim Armstead, R-Kanawha, ran for speaker in January and told The Associated Press that he would do so again after Thompson's announcement.
"There are a number of conservative Democrats in the House who have not been pleased with the direction that some of the policies have gone in the House in the last several years," Armstead said.
Thompson is tentatively expected to resign from the House on June 15. At that point, Tomblin will have 10 days to call the House into session to elect a new speaker.
Normally, that call could coincide with monthly legislative interim meetings, set for June 19-21. However, June interims will be held in Wheeling, to commemorate the state's 150th anniversary, and that will require Tomblin to call the session in Charleston either immediately before or after the interim meetings.
Typically, House Democrats meet in closed-door caucus the evening before to select a nominee, who then is unanimously backed by Democrats in the floor vote.
Miley said he does not anticipate a contentious speaker's race.
"I frankly believe that when the position is vacated, the Democrats will get together, and get behind the one person they believe is best to lead them in the House of Delegates," he said.
This could be the first seriously contested race for speaker since former Delegate Scott Varner, D-Marshall, faced Thompson in the December 2006 Democratic caucus after former speaker Bob Kiss, D-Raleigh, did not run for re-election.
Varner, who had been House majority whip under Kiss, remained in the House for six years afterward, but never again held a leadership position.
The Department of Veterans Assistance was elevated to a cabinet-level position in state government in 2011. Gwinn had led the department for a decade before that, but said Thursday his health will force him to leave.
"I have to [retire]," Gwinn said. "I have had eight operations in the last six years. ... I look forward to working with Mr. Thompson."
Staff writer Kate White contributed to this report. Reach Phil Kabler at ph...@wvgazette.com or 304-348-1220.