Updated at 6:30 p.m. with details throughout.

AUSTIN -- Whether Texas drastically overhauls its property tax system could come down to one lawmaker -- Sen. Kel Seliger, an Amarillo Republican.

On Thursday morning, lawmakers in the House and the Senate appeared ready to vote on bills to slow property tax growth for home and business owners by limiting revenue collections from local governments and school districts.

But the plans were scrapped when it became clear that the Senate lacked the votes to bring the bill up for consideration, ostensibly because Seliger, who previously served as a city mayor, would not sign on.

Seliger even had a private meeting with House Speaker Dennis Bonnen Thursday afternoon, just before Bonnen announced the House and Senate needed more time to deliberate.

"We are respectfully working with the Senate on this issue," Bonnen said.

The House is scheduled to vote Monday on its property tax bill.

The property tax legislation is the priority of top Republicans, including Gov. Greg Abbott, who have promised to slow skyrocketing tax bills. But local officials have strongly opposed the plans, saying they would rob city and county budgets of dollars to provide critical services like police and fire protection.

Early Thursday, Lt. Gov. Dan Patrick, who presides over the Senate, lamented the single Republican opponent without using Seliger’s name.

“It is frustrating,” Patrick told Lubbock KFYO radio host Chad Hasty, “to have one Republican block the will of the people and even the will of their district.”

Patrick noted that Senate rules require 19 members to agree to debate a bill. He said he has 19 Republican members but only 18 votes secured.

Patrick and Seliger have long been at odds. Their feud was reignited in January when Patrick stripped Seliger of a committee chairmanship after he said the Amarillo Republican had insulted one of his staff members. Seliger, however, said it was retaliation for voting against Patrick’s priority bills in the past when his constituents had asked him to support local control and public education.

Last week, Seliger told The Dallas Morning News he was against the priority legislation that would cap property tax growth for local governments and school districts at 2.5%, calling it too punitive. The bills would allow the cap to be exceeded if voters approved it in an election. Currently, local governments can increase property tax revenue by up to 8% a year without the threat of an election.

On Thursday, Seliger said he was still against a 2.5% cap but was trying to find a compromise.

"If there's a way I can help, then great," he said. "So what we've been doing this morning is talking to county judges and school district people about what we can live with, because there's a tremendous sentiment and inertia to do something about property taxes."

In 2017, the Legislature debated similar proposals to cap local property taxes. The Senate’s version of the bill had a 4% revenue cap, and at the time, Seliger and Republican Sen. Charles Perry, from Lubbock, voted along with Democrats to oppose the bill.

But Perry said Thursday he was encouraged by some of the exemptions in the bill for rural and small cities.

The bills, as written, don't apply to local governments that have less than $15 million in revenue.

“The big deal for me is that $15 million carve out,” he said. “It gets most of my little guys.”

Notably, Seliger’s opposition would be meaningless if Abbott calls a special session, when the 19-member rule no longer applies and the bill could be brought to the Senate floor with a simple majority.

Compromise and deal breakers

On Thursday morning, the House was scheduled to take up its version of the bill, sponsored by Rep. Dustin Burrows, R-Lubbock. But the vote was delayed once word circulated that the Senate was considering its own vote.

Grand Prairie Rep. Chris Turner, chairman of the House Democratic Caucus, said he hoped the pause would allow for more productive changes to be made.

"Hopefully, the postponement means that a sincere policy discussion is taking place on this bill to minimize the negative impacts on local governments," he said. "We've heard from mayors, county judges and others that any of the revenue cap proposals that have been floated thus far are going to be harmful to the communities they represent."

Throughout the day, House members circulated amendments that could lead to a compromise.

Democrats are pushing exemptions for public safety or proposals to raise the revenue cap to 5.5% or 6%.

Burrows filed an amendment that would tie the rate cap to inflation.

Even House Democrats expressed a willingness to compromise on a path forward.

"A 2.5% cap in and of itself is not a deal-breaker for me," said Rep. Eddie Rodriguez, D-Austin. "It depends on what else you add to it so it doesn't cripple cities or counties."

Rodriguez, who voted against the bill in the House Ways and Means committee, said he would like to see some concessions, like an exception on public safety spending or a guarantee that any revenue growth cap would factor in inflation.

Lawmakers this session are considering a variety of other plans to rein in property taxes, including bills to increase the homestead exemption, cap appraisal growth and buy down property tax rates.

This week, Abbott, Bonnen and Patrick endorsed a plan to increase the state sales tax by one penny, generating $5 billion, to lower property tax rates.

Meanwhile, Abbott weighed in Thursday to let it be known where he’s willing to compromise and where he’s drawing the line.

He said he "absolutely" wanted schools to be included in the legislation, but the Ways and Means committee stripped school districts and special taxing districts from the bill.

"Gov. Abbott has made clear from the beginning that in order to achieve real property tax reform, there must be a cap on school districts’ ability to raise taxes. Regardless of which bill this cap is placed in, limiting school districts’ ability to raise property taxes is essential to achieve lasting property tax reduction," spokesman John Wittman added.

But Abbott demurred when asked about whether the Legislature should hold the line at 2.5% -- a limit he championed during his campaign.

"You know, I'm not talking to you about this," when asked if he would require the bill to have a 2.5% cap. "The information will be pretty clear pretty soon."