There were claims this could ease the impact on families and schools in the county.
The children and young people’s services select committee agreed to ask cabinet member councillor Peter Griffiths – who will make the final decision – to explore the options for phasing in budget reductions.
It is also urging him to seek reassurances from public trans-port providers on the future of those services used by pupils.
The select committee will press for local solutions to be sought if there are specific local problems.
Among concerns expressed during the debate were possible problems faced by some families who had already chosen a church school for this year, before the proposal to cut subsidies was known.
The proposal is to withdraw transport funding from pupils attending denominational schools, except for those from low-income families, from September.
Protection is also proposed for current year-10 pupils. Mr Griffiths told the committee he was a “passionate believer” in consultation, and would be listening to what was said.
But he also pointed out that providing transport was not a statutory obligation for the county council.
“This is something we provide within the means we have at our disposal, which at the moment are diminished,” he added.
Mary Reynolds, director of the diocese of Arundel and Brighton Catholic schools service, said: “The long-term impact has severe consequences for us.”
The select committee heard the cost of transport provision for church schools for 2010-11 was about £650,000, and the income was £120,000.
Bob Lanzer, councillor, said the council needed to say more about how it could mitigate the impact of the proposals. This could include influencing and contributing to school transport plans.
Worthing councillor Bob Smytherman said he was a passionate believer in church schools, but how far should the taxpayer subsidise people to go to the school of their choice.
The most important thing was to protect the most vulnerable, so they could go to the school of their choice.
“I would hate to think faith schools will become elite schools,” he said.
Bob Burgess said he was concerned about parents of pupils who would be going to faith schools this September.
Criteria for choice were being changed after the choice had been made.
Mr Griffiths said his impression was that parents chose a school because it was a faith school, not because it got free transport.