HARRISBURG — A bill in the state Senate that would allow more children to attend private and religious schools with taxpayer help encountered the first signs of trouble Tuesday, just hours after hundreds of private school students shepherded by parents and teachers went to the Capitol to push for passage of a top GOP priority.

Gov. Tom Corbett spoke privately to Republican senators, as questions swirled around whether the bill had enough votes to pass or whether Corbett even supported it. Shortly after Corbett met with Republicans, a scheduled Tuesday vote on the bill was delayed until at least April 26 so that the bill could be revised, Senate Majority Leader Dominic Pileggi said.

The bill, which is supported by most Republicans and possibly a few Democrats, would create one of the nation’s biggest school-voucher programs in the country, if not the biggest.

Supporters say the bill will help families get their children out of struggling or unsafe public schools, although detractors contend it will be very costly for taxpayers while doing little, if anything, to improve the quality of public education or student test scores in Pennsylvania.

Corbett would not tell The Associated Press what he told senators, but senators said Corbett pledged support for the bill, if not a promise to sign it.

“The governor expressed an interest in making clear to the caucus his support for the bill and ... beyond the principle of school choice and vouchers that he was specifically interested in,” Pileggi said.

Republicans control the Senate 30-20, but a handful of Republicans appear to be against the bill. Pileggi would not say what concerns from senators drove the need for changes or what kind of changes senators wanted.

Senate Minority Leader Jay Costa said he believes support for the bill began to erode when the cost to the state and to school districts dawned on senators at a time when Corbett has already proposed cuts in state aid to public schools.

“There’s a sincere question about the cost and that’s where support on both sides of the aisle has waned,” said Costa, D-Allegheny.

Republicans project that the bill, which still would need House approval, would cost taxpayers more than $730 million in the first four years, when it would gradually expand to serve more children. It underwent a major amendment Monday that the chief sponsor, Sen. Jeffrey Piccola, R-Dauphin, said was designed to appease senators who worried that it would be too expensive and did not do enough to help middle-class families.

However, Costa said he believes the bill will still be more expensive than Republicans are projecting.

Pileggi maintained that the bill remains a top priority of the Senate GOP, and that any changes will be minor.

“It is something that the governor would like on his desk at the same time we pass the budget or before we pass the budget, and we intend to work to accomplish that goal,” Pileggi said.