(State House News Service) -- Favored spending initiatives that help reduce the strain on Massachusetts schools did not make it into Gov. Charlie Baker's annual budget proposal at levels desired by some of the lawmakers who will play key roles crafting next year's final budget.

Baker's budget proposal consolidates grants offered to school districts and eliminates a grant program for kindergarten expansion while increasing the state's funding for local schools.

"I think the reality for a lot of these districts is they rely on this money as a separate source of local aid," said Rep. Paul Brodeur, a Melrose Democrat, speaking in support of kindergarten grants.

The administration justified the cuts to the kindergarten grants by noting 85 percent of school districts offer full-day kindergarten and those kindergarten students are funded through the state education aid account known as Chapter 70.

Education Secretary James Peyser faced House and Senate budget-writers at a hearing Tuesday at Greenfield Community College, where he maintained the administration's budget is a net benefit to school districts.

"There's a significant increase," Peyser told the News Service after testifying. "I mean some districts are going to be up and some are going to be down. There's no question about that."

Senate Ways and Means Assistant Vice Chairwoman Patricia Jehlen argued the Chapter 70 funding formula has "not kept up with the realities" faced by school districts. She said the foundation budget used in the formula to meet the needs of the 1993 education reform law is underfunded by $2 billion and said the Baker administration plan would affect districts disproportionately.

"The actual total aid to local districts is about the same, but the cuts are distributed unequally," said Jehlen, a Somerville Democrat.

Jehlen told the News Service the Baker budget would hurt rural and urban districts in the areas of charter school reimbursements, homeless student transportation and regional district transportation.

House Vice Chairman of Ways and Means Stephen Kulik, a Worthington Democrat, voiced his support for regional school transportation funding, which receives $18 million less in Baker's budget than the amount the Legislature approved last summer.

Facing a deficit late last year, former Gov. Deval Patrick used his executive 9C powers to cut regional school transportation, which the Legislature had increased in the fiscal 2015 budget. Baker's fiscal 2016 budget would keep it at that reduced level, according to Kulik.

"We were very disappointed with Gov. Patrick's 9C cuts of the entire $18 million increase," Kulik told the News Service after the hearing. He said, "That is a very popular account, without question."

Peyser also discussed the plan to consolidate nearly one dozen education grants into a $17.5 million Partnership Schools Network grant account, which he said would muster a "critical mass of flexible resources" for "ambitious reform plans."

The consolidated fund would include $1.6 million less than the 11 separate items following the executive branch budget cuts this year to deal with a midyear deficit.

"I think we need to start consolidating a lot of things," Rep. William "Smitty" Pignatelli, a Lenox Democrat, told the News Service. "But we need to make sure that small towns like I represent are not at a competitive disadvantage with that same application for that finite dollar with some larger community or larger school district."