The smoking ban seemed to have recovered from a near-defeat Friday but staggered further Monday before it passed 91-48.
Now in its weakened state, the bill still needs a final House vote before it goes to the Senate, where it faces an uphill battle to survive.
Myra Crownover, the Lake Dallas Republican pushing the measure, said the ban is needed to protect workers and other people regularly exposed to secondhand smoke.
"Our attempt is to save lives. Secondhand smoke kills," Crownover said, vowing to try to get the bill back to its original, stronger form. "Nothing is ever finished until it signed by the governor."
The biggest fight came over an attempt to exempt bars, which Crownover argued would have defeated the purpose of the bill. The bar exemption had been placed in the bill Friday, but was removed after negotiations over the weekend.
But Crownover later accepted an amendment that allows property owners -- not always the bar or restaurant operator -- to decide if smoking will be allowed. The owner would have to post a sign in a conspicuous place noting that smoking is permitted.
Crownover acknowledged that the exemption punches a huge hole in the ban.
"I will work very hard," to take it out, she said.
The bill includes other exemptions for bingo and VFW halls and bars that offer their employees health insurance. Cities could also opt out if local voters can get the issue on the May 2008 ballot.