Ryan Ferns, a co-chair of that committee, told reporters late Monday he had proposed a compromise to some House leadership but Ferns did not reveal details.
Union leaders haven't said whether they're calling for an end to the strike, pending a ceremony at the governor's office later Tuesday.
Schools systems in almost all of the state's 55 counties have announced they will remain closed Tuesday.
After nine school days of protest, it appears the teachers have won, at least in terms of a pay raise, with West Virginia lawmakers agreeing to a 5% pay increase for all state employees.
When state union leaders urged teachers to go back to work last week, they refused. "We just need to see it in writing", she said. "The governor's basically following that belief".
"While every state and community is going to be different, what we do know is that educators want to be in the classroom with their students". Robert Plymale, a Democratic committee member, said referring to the $6.9 million difference.
Rachel Stringer, a stay-at-home mom from Cross Lanes, said her biggest challenge is making sure her children don't forget what they've learned this school year. "This has been the fiscally responsible thing to do, in my opinion, to get us to the point we're at today".
"In our case, it's not just a pay raise", Priest said.
The West Virginia Legislature faced a standoff over how much of a pay raise to offer striking teachers and educators. The size and density of the crowds has prompted a "capacity concern from Capitol Police and the West Virginia Fire Marshal".
Lawrence Messina, a spokesman for the state Department of Military Affairs and Public Safety, said more than 5,000 people had arrived by noon. Capitol Police and organizers are working to "ensure manageable conditions this afternoon", the agency said.
West Virginia teachers began the statewide strike on February 22 - the first in nearly 30 years - after Gov. Justice signed a 2 percent salary increase for teachers for the next fiscal year, and a 1 percent increase for the following two fiscal years.
In Oklahoma, teachers are weighing a possible walkout over budget cuts that have led to four-day school weeks in that state, and left teachers' average salaries there trailing those in West Virginia. School service personnel are also walking out. Along the way, the teachers disregarded union leaders' advice to return to work when the governor first promised them the raise last week, deciding in meetings at malls and union halls and in Facebook groups that they would stay out until their raise was enacted in law.
CHARLESTON, WV (WVNS) - Gov. Jim Justice (R-WV) has announced that a deal has been reached to get teachers back in the classroom.
The House voted not to adopt the 4% version of the bill.
The agreement was signed by each member of the appointed conference. The measure now goes back to the legislative houses for approval. The also voted to have the raise to begin on July 1.
Gov. Jim Justice is expected to quickly sign the deal. The suggestion was rejected by the Republican leadership.
Randi Weingarten, president of American Federation of Teachers, said the deal was a "huge breakthrough" for school employees and for doing what's right.
Few states can boast teacher salaries lower than West Virginia.