Stymied in their initial efforts to cut Fulton County property taxes, House Republicans have introduced a new measure that could save tens of thousands of homeowners money.

The bill would double the county’s property tax homestead exemption to $60,000 over three years, if voters approve in 2014. When fully implemented, that would mean the owners of homes valued at up to $150,000 would pay no county property taxes.

Republicans say the tax cuts would force Fulton to trim spending.

“Clearly there is reason to cut the fat and give relief to taxpayers,” said House Speaker Pro Tem Jan Jones, R-Milton, who sponsored the bill. “I think this is a measured approach to help all homeowners throughout Fulton County, from north Fulton to Atlanta to south Fulton.”

Democrats say her bill would force dramatic cuts in funding for libraries, Grady Memorial Hospital and other services.

“Citizens are going to see a massive cut in services,” said Rep. LaDawn Blackett Jones, D-College Park.

Republicans have long sought to shrink the size of Fulton County government, which they say is bloated and wasteful. To that end, Jones and other north Fulton Republicans introduced House Bill 170 earlier this year.

The measure would have raised the county homestead exemption from $30,000 to $60,000 over two years. It also would have capped the county property tax rate for two years and required five votes on the seven-member County Commission to raise taxes thereafter.

Jones twice postponed calling HB 170 up for a vote in the full House and later withdrew it. Democrats said she couldn’t muster the 120 votes needed to pass. Jones denied that Tuesday, saying the bill had a legal flaw: The state can’t cap a county’s tax rate. So she’s trying again with House Bill 541.

The new bill would still double the county’s property tax homestead exemption to $60,000. But it would spread the increase out over three years instead of two. And it would not include a cap on the property tax rate. Voters would still have to approve the homestead exemption increase in 2014 for it to take effect.

So it would still need 120 votes, and Republicans hold 118 seats in the House.

Jones plans to introduce a second bill that would require a vote of five commissioners to raise the millage rate. That provision does not need a supermajority to pass, she said.

An Atlanta Journal-Constitution analysis of data from the county tax assessor’s office found doubling the homestead exemption would cut taxes for more than 100,000 people. But county officials say it would cost Fulton $48 million in tax revenue and force cuts to popular services.

County Commission Chairman John Eaves criticized what he said was state lawmakers’ micromanagement of county affairs.

“It’s counterproductive,” Eaves said. “It’s mean-spirited.”

State Rep. Harry Geisinger, R-Roswell, said Fulton would still be able to deliver essential services. He said the county hasn’t cut its payroll enough since four new cities formed in Fulton in the 2000s, reducing the area where the county provides services such as police, fire protection and parks.

Geisinger said the county should start shedding employees through attrition.

“It’s been a works program, just like MARTA has been, for years,” he said.

The homestead exemption proposal is just one of a series of bills Republicans are pushing to reshape Fulton. Other bills would make it easier to fire county employees, make the tax commissioner an appointed position instead of an elected office and redraw commission districts in a way that potentially could give Republicans a majority.