After wrapping up the afternoon of debate, the House then adjourned until Monday, a signal that the majority Republican chamber's leaders don't expect to offer much more in the way of revenue-raising measures for the Democratic governor.
Edwards called lawmakers into the special session aiming to raise $600 million for the financial year that begins July 1, to stop what he describes as deep cuts to health care, education and public safety programs.
The House tax committee has stalled many measures sought by Edwards, particularly income tax changes that could hit middle- and upper-income residents.
The biggest-ticket bill passed Thursday by the House would raise taxes on health care organizations known as HMOs, raising about $189 million.
"It will take us a good portion of the way down the road," said Rep. Walt Leger, D-New Orleans. But he added it wasn't enough "to solve our budget problem."
Another approved measure would change the calculation of interest on tax overpayments. A third bill would lessen the tax break for homeowners charged an assessment on their insurance to cover debts of the state's property insurer of last resort.
The bills head to the Senate.
The session is short, wrapping up by June 23. Senators, who are more open to taxes, could try to tweak the bills sent to them with Thursday's House votes to raise more money. But they can only work with what they receive, because tax increases must originate in the House.
Many Republican lawmakers in the House are resistant to tax measures, after the Legislature raised more than $1.2 billion for next year's budget with tax hikes passed in a special session called by Edwards earlier this year. They say they want to wait and see how much money comes in from those prior increases.
Others say they want a larger rewrite of the state's tax and budget structure.
"I can support revenue with reform in our policy," Rep. Barry Ivey, R-Baton Rouge, said during a tax committee hearing.
But he said he couldn't say reform is coming later and vote to raise taxes now.
"That doesn't work back in my district," Ivey said.
Lawmakers haven't started deciding how they will spend any money they raise. Gaps in next year's budget remain for the TOPS college tuition program, college campuses, K-12 education, the safety-net hospitals that care for the poor and uninsured, and prison programs.
After the tax votes, the House agreed to a multibillion-dollar construction budget to finance roadwork, building repairs and projects around the state.
In the final hours of the regular legislative session, the House refused to pass the bill, forcing lawmakers to start the process over when the special session began. House leaders said Senate changes put the bill in such disarray that it needed a rewrite. Senators accused the House of refusing to negotiate.
Ways and Means Committee Chairman Neil Abramson, who was blamed for tanking the bill, has tried to defuse the tension in recent days, by getting the bill to the Senate quickly.
But before the House voted 90-8 Thursday for the construction budget, Rep. John Schroder, R-Covington, slammed the measure as being bloated, continuing to give the governor the ability to pick and choose which projects get financing.
"This is the bill that controls everything else in how you frickin' vote, and it's really a shame," Schroder said. "I don't like this process. I think it's dirty. I think it smells."
Abramson, D-New Orleans, said while the bill hasn't been slimmed enough to match projects to available money, it's smaller than in years past.
"We're on the path toward right-sizing this," he said. "We'll pick up this process again next year."