Lawmakers in the House agreed to stop stalling the measure and intend to schedule it for a Monday hearing.
Without the bill, any dollars raised couldn't be spent to stop health and education program cuts next year.
But until Thursday, House Appropriations Committee Chairman Cameron Henry hadn't even filed the budget measure for consideration. House leaders had said they didn't want to craft a plan to spend new tax dollars until the state's income forecasting panel, the Revenue Estimating Conference, formally recognizes the money as available for spending.
They gave up on that idea amid pushback from the Senate.
Senate leaders say formal recognition of the tax dollars can happen after the special session ends and before the July 1 start of the new budget year.
"The (Legislative) Fiscal Office is advising us all through the process. I don't know why we can't use those numbers like we have done forever," said Senate President John Alario, R-Westwego.
Henry, R-Metairie, gave in and said he doesn't expect the estimating panel to meet until after the legislative session ends next week.
"In an ideal world, I think it's prudent for us to have the Revenue Estimating Conference meeting. I don't think time really allows for that at this point," Henry said.
No tax bills from the special session have reached final legislative passage — or been signed into law by Gov. John Bel Edwards — so the income estimating panel has nothing to forecast for spending yet.
Senate Finance Committee Chairman Eric LaFleur, D-Ville Platte, said if the House waited on an updated income forecast reflecting tax bills that haven't passed, "they'll be waiting a long time."
He described Henry's initial plan to wait as "ludicrous."
"I don't know what they were thinking," LaFleur said Thursday.
A meeting between House Speaker Taylor Barras, Alario, Henry and LaFleur ended talk of needing a Revenue Estimating Conference meeting before session ends. And Henry filed the budget bill.
"Everybody's working together well," Henry said. "I don't expect much drama."
The House and Senate haven't reached a deal yet on taxes, so Henry said the House will work with the $220 million or so the House has agreed to raise so far.
Edwards has asked for $600 million to stave off cuts to the safety-net hospitals that care for the poor, the TOPS college tuition program, K-12 education, public safety programs and college campuses.
Senate leaders want to raise $450 million.
The special session must end June 23.