HARRISBURG — Hundreds of private school students shepherded by parents and teachers went to the Capitol on Tuesday to push for the state Senate’s passage of a bill that would allow more children to attend private and religious schools with taxpayer help.

The bill, which is supported by most Republicans and possibly a few Democrats, was poised for a vote later Tuesday in the Senate. It would create one of the nation’s farthest-reaching 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 say it will be costly for taxpayers while doing little, if anything, to improve the quality of public education or student test scores in Pennsylvania.

The bill’s chief sponsor, The bill is projected to cost taxpayers $730 million in the first four years, when it would expand to serve more children.

Under the bill, tens of thousands of children from low-income families — about $28,600 a year or less for a family of four — would be eligible to get taxpayer help paying for private or religious school tuition, or be able to switch to another public school district.

In the fourth year, children of middle-income families — about $67,000 a year or less for a family of four — would be able to get tuition help as well, while school districts would be able to apply for money to help establish their own voucher programs.