This is the first time in two years that the school system has had to urge the council to fully fund its budget. Superintendent Jerry D. Weast proposes a $1.99 billion operating budget for the school system. County Executive Isiah Leggett (D) recommends $1.97 billion for schools — $19.7 million less than Weast’s proposal.

The school system, in response to Leggett’s proposal, has launched an ambitious effort to get the money. Advocates rallied on the steps of the Council Office Building in downtown Rockville before a budget hearing last week to urge full funding. Much of the testimony before the council was from people lobbying for the full $1.99 billion.

At least one council member said it is unlikely that the school system will get all that it wants.

‘‘I think it’s a reach to expect full funding in this particular political climate,” said Councilman Roger Berliner (D-Dist. 1) of Potomac. ‘‘They’ve demonstrated that they’re a powerful voting constituency, but you run the risk of overstating your case by suggesting that any cut harms children.”

Councilman Michael J. Knapp (D-Dist. 2) of Germantown, chairman of the council’s Education Committee, has vowed tighter scrutiny of the school system’s budget. As for last week’s rally and testimony for full funding, Knapp is taking a wait-and-see approach.

‘‘[The rally] provides a level of awareness of just how the community feels about the MCPS budget,” he said. ‘‘I don’t know if it adds votes or take votes away. I’m trying to put the pieces together. Everybody wants you to have an answer in the first four days.”

Councilwoman Valerie Ervin (D-Dist. 5) of Silver Spring, a school board member for two years, takes a different approach. She said this week that she’s not gung-ho for full funding, but she does not want the budget cut ‘‘just for the sake of cutting it.”

The April 11 rally was ‘‘a really good opportunity for the council to hear from constituents they normally don’t hear from,” Ervin said, referring to the teachers, principals and school workers who rallied and commented during the budget hearings.

In an April 6 letter to Council President Marilyn J. Praisner (D-Dist. 4) of Calverton, Leggett suggested where some cuts could made, including:

*Reduce the communications department budget by $1 million.

*Cut the organizational development program by $9.2 million.

*Phase in the hiring of high school counselors and assistant elementary school principals over two years, which would free up $2.3 million.

In his own memo to the school board on April 10, Weast flatly disagreed with Leggett’s recommendations.

‘‘The county executive’s recommended budget was problematic from the beginning and the proposed reductions only make things worse,” he wrote. ‘‘Nowhere within the county executive’s newly proposed reductions or the original budget recommendations was there an appreciation for the increased demands and challenges facing our children in Montgomery County.”

Leggett’s proposal includes $117 million — or 6.3 percent — more than last year’s budget. Of the school system’s request, roughly $122 million is for payroll and to pay for health care for retired workers, Weast wrote in the memo.

Advocates this week expressed pessimism about the possibility of the council approving Weast’s full request.

‘‘I’m worried that [the budget] won’t be fully funded,” said Bonnie Cullison, president of the county’s teachers union. ‘‘The question is what will that final number be, and how much damage will that final number do.”

Jane de Winter, president of the County Council of PTAs, figures the council will come up with more money than Leggett has proposed, but the budget will still fall short.

‘‘It does not have to be schools versus the other agencies,” de Winter said. ‘‘The bottom line is that they have the money right now and they’re making the choice not to fund the budget.”