The Loudoun County Board of Supervisors voted Wednesday to direct County Administrator Tim Hemstreet to prepare a fiscal 2014 budget that would lower the county’s real property tax rate and leave the public schools facing a projected $68 million shortfall.

Despite concerns expressed by some Loudoun School Board members — who have warned that such extensive cuts would have a profoundly negative effect on the school system — the supervisors followed a board committee recommendation that would keep the county budget stable and leave the schools to absorb the cuts needed to lower taxes.

The board’s five-member Finance and Government Operations Committee voted in September to recommend that the board pursue a budget that would lower the county’s property tax rate by 3 cents per $100 of assessed value — cuts that would be made possible by providing about $2.5 million less to the school system.

But the current adopted schools budget projects that the system would need about $62 million in additional funding for fiscal 2014 to keep up with the arrival of 2,500 new students and the opening of two elementary schools.

Despite unified campaign promises of fiscal responsibility and lower taxes, the nine Republican supervisors were far from unanimous during their budget discussion Wednesday.

Three board members — Vice Chairman Janet Clarke (R-Blue Ridge) and supervisors Geary Higgins (R-Catoctin) and Matt Letourneau (R-Dulles) — voted against the motion to create a budget that would leave the school system alone facing reductions. Letourneau’s alternative motion to seek an equalized budget for the county and the school system failed, but it split the board with four votes of support.

The division suggests that the coming budget season could again prove challenging. In April, after a prolonged and tense budget process, county supervisors adopted a $1.8 billion county budget, including $809 million for schools.

The reconciled school budget was $22 million less than the $831 million plan first proposed by School Superintendent Edgar B. Hatrick III. County leaders cautioned the School Board to prepare for even deeper cuts in fiscal 2014.

But Clarke, who suggested that the supervisors should consult with the School Board to come up with “an alternative scenario” that was more realistic, said it was a waste of time to create a budget that would leave the schools grappling with such a wide funding gap.

Such a proposal “isn’t even remotely possible,” she said.

Letourneau expressed similar doubts, noting that even achieving an equalized county budget — meaning that average county taxpayers would see no change in their real estate tax bills — would be a challenge. The schools would still be facing a $50 million deficit in that scenario, he said.

“I think this is just a question of whether we take a very extreme position, which I think is frankly unfair,” he said.

Letourneau agreed that the schools would need to fulfill their promise to pursue additional cost-saving measures, but he said that pursuing a 3-cent reduction was going too far.

“I think the equalized tax rate sends the message almost as effectively,” he said.

A majority of supervisors ultimately supported the proposed budget guidance and said it was important for the school system to understand that further cuts would be necessary no matter what — even if a 3-cent tax rate reduction were ultimately deemed impossible.

Supervisor Shawn Williams (R-Broad Run) said it was important to send a message to the schools to look carefully at where the money is going. The funds might not be going to classrooms or to teachers but rather to an “overly bloated administration,” he said.

“I want to continue to keep our high quality of schools, but something’s got to give,” Williams said.

Supervisor Ralph Buona (R-Ashburn), who leads the Finance and Government Operations Committee and proposed the motion Wednesday to follow its recommendation, questioned the idea of the School Board facing a $68 million shortfall.

“Let’s not forget, they’re asking for a $63 million increase,” he said. “This isn’t bullying. I think we owe it to the School Board to let them understand where our mind-set is and what our expectations are.”

Buona pointed out that the county government has also been “squeezed and squeezed” in the past and said that it was time for the School Board to “start following suit with what we’re doing on the county side.”

The proposed fiscal guidance could help ensure that as the School Board prepares its budget, “we are at least somewhere in the same universe,” Buona said.

Having received their fiscal guidance, Hemstreet is expected to present a proposed budget to supervisors in February.