A regional grant program backed by leaders in business, education and government was approved in the Virginia House Tuesday, despite some opposition from Republicans troubled by what they described as free-market meddling.

“The way to spur economic growth in Virginia is to reduce taxes for businesses and working families and let them keep more of their hard-earned dollars,” Del. Ben L. Cline (R-Rockbridge) said after voting against the grant program.

One bill under consideration would set up a state board to establish regional councils that can apply for money for projects, such as job training centers. A second would give cities and counties that work together up to half of the income tax revenue from new jobs they have a hand in creating.

Business leaders would run the board and councils, but board members from the Senate, the House and the governor’s Cabinet would each have veto power.

Gov. Terry McAuliffe (D) supports the program, which his two-year budget proposal would fund with nearly $40 million.

Although an early version of the program would have paid grants directly to companies, Senate Majority Leader Thomas K. Norment Jr. (R-James City) said the bills now call for local matches. The system is intended to prevent what he called “hiccups” in economic development deals, and to encourage localities to work together.

“This is a fairly significant cultural change in the way we do regional government,” Norment said during a committee meeting Tuesday. “This needs to be a long-term commitment, and I am absolutely persuaded of the viability of it.”

Lawmakers and officials who support the grant program talked up the need to diversify the state economy. Sen. Janet D. Howell (D-Fairfax) said across-the-board federal funding cuts known as sequestration provided a “rude awakening” for Virginia businesses, which until now has relied largely on federal defense spending.

Todd Stottlemyer, who is CEO of the Inova Center for Personalized Health at Inova, said the newest campus of Northern Virginia’s largest hospital system is a collaboration with universities and others, similar to what could be created through the new grants program.

“GO Virginia will help us jump start more collaborate initiatives,” he said.

After hearing the glowing testimony, Sen. Emmett W. Hanger Jr. (R-Augusta) asked whether anyone opposed GO Virginia — to laughter from the morning crowd of lobbyists and lawmakers.

But a few hours later, Del. Robert G. Marshall (R-Prince William) spoke against it on the House floor. He and a handful of colleagues voted against the bills, both of which passed the overwhelmingly Republican body with 93 yes votes.

“We are entering into the marketplace as a government entity – at arm’s reach, but it’s nevertheless the state asking our subordinates in the localities to do this,” he said.

John O. “Dubby” Wynne, chairman of the Hampton Roads Community Foundation and former chief executive of Landmark Communications, has been the primary driver of the program. He sits on the Virginia Business Higher Education Council, which hired the lobbying giant McGuireWoods to craft the bills, with input from lawmakers.

Both bills say localities can only win grants for proving they had a hand in creating at least 200 jobs and a $25 million investment. The Senate version would lower the bar to 25 jobs and a $1 million investment for communities with high unemployment.

The Senate version gives their members equal representation on the state board as the House. In the House version, their members have a one-delegate advantage.