The suit comes after the administration rejected Browning's public records request for documents relating to the plan, invoking its executive privilege.
"The Legislature is a branch of government and we deserve to be part of the process," Browning said.
Supporters and skeptics alike should be demanding to see the administration's work on a financing plan for Green Mountain Care in the interest of transparency and so the work can begin to be vetted, she said.
The House of Representatives gave preliminary approval to a wide-ranging health care bill that supporters say positions the Legislature to pass laws during the next session that will underpin Vermont's planned universal health care program.
A debate on the House floor late Wednesday hinged on a provision to compel Gov. Peter Shumlin's administration to deliver a financing plan for Green Mountain Care, as the program is known.
"Our concern is that we get the best proposal, not that we get the earliest proposal," said Rep. Janet Ancel, D-Calais, chair of House Ways and Means. Reviewing an incomplete plan would not be a good use of legislators' time, she said.
The bill, S.252, requires the Shumlin administration to produce a financing plan by January 2015.
"In plain language, if the administration hasn't delivered a financing plan by that time, the clock has run out," said Mike Fisher, D-Lincoln, chair of the House Health Care Committee.
Shumlin has said he doesn't want to release a plan that isn't ready, but administration officials have said they will be prepared to deliver by the first of the year.