Under current income guidelines, children of families of four making less than $51,000 are eligible for the free program. Children currently enrolled under that definition could continue the program.
For future enrollments, the bill would change the cutoff to 100 percent of poverty, which is about $23,550 for a family of four, or $19,530 for a family of three.
Early education advocates say that could cut the number of children eligible for the program by at least a third.
House Republicans floated a similar proposal in 2012. At that time, Burr said narrowing the income eligibility would allow the state to focus its resources on children most in need of assistance.
It could also help the state out of a legal fight with Superior Court Judge Howard Manning, who ruled in 2011 that the state has a constitutional duty to provide free pre-kindergarten to all at-risk 4-year-olds.
In 2012, the state Court of Appeals unanimously upheld Manning's ruling. The state Supreme Court agreed last month to hear the case.
Last year, under the current definition, the number of at-risk 4-year-olds in the state was estimated at 67,000. The state allotted funding for only about 26,000 seats.
Covering all of them would likely cost the state an additional $300 million a year. But a change in the definition of "at-risk" could allow the state to be in compliance with Manning's ruling without spending extra money.