After an hour of debate that showed a marked lack of enthusiasm for the measure, the Texas House voted unanimously Sunday evening on a property tax break worth about $125 to the average homeowner.

In a 136-0 vote, the House favored Senate Bill 1, which would raise the homestead exemption from $15,000 to $25,000 if voters approve an amendment to the state constitution in November. The House also passed Senate Joint Resolution 1, a related measure, on a 138-0 vote.

The measure is one part of a $3.8 billion tax relief package agreed to by the House, Senate and Gov. Greg Abbott last week after months of debate between the chambers over whether to focus efforts on property taxes or the sales tax.

The original Senate plan, from Senate Finance Chairwoman Jane Nelson, R-Flower Mound, would have pegged the homestead exemption rate to 25 percent of the state’s median home market value, which would have boosted it to about $33,000 in 2016. Lt. Gov. Dan Patrick’s office has said that that would have saved the average Texas homeowner $207 in property taxes next year.

The Texas Tribune thanks its sponsors. Become one.

House Ways and Means Chairman Dennis Bonnen, R-Angleton, coolly laid out SB 1 on Sunday, making clear to fellow House members that he did not think it was the best approach to cutting taxes because the state would be on the hook for paying school districts to cover their losses in local tax revenue. For months, he has criticized the idea as misguided, predicting that most homeowners either won’t notice the tax cut on their property tax bills or will view it as underwhelming.

“We are lessening the pain to a small extent,” Bonnen said. At another point, he noted that the measure was “shifting the tax burden” rather than actually cutting taxes.

Near the end of the debate, Bonnen told lawmakers that the bill was worth supporting as long as proponents didn’t oversell its impact.

“Don’t make the mistake that I have made three times before,” Bonnen said. “Three times we’ve cut property taxes and I’ve gone home and said, ‘I’ve cut your taxes.’” He urged House members to tell constituents that lawmakers did what they could to address the issue but that local entities are where concerns about property taxes should really be focused.

The measure now heads back to the Senate, where senators will have the choice of concurring with House amendments or calling a conference committee to hash out a compromise measure.

Shortly after the House passed the Senate’s tax relief measures, the Senate passed the other part of the tax cut deal, Bonnen’s House Bill 32, in a 24-6 vote. The bill cuts the franchise tax rate by 25 percent.