Virginia Gov. Robert F. McDonnell proposed Monday shuffling millions of dollars from public schools and health care to his top priorities of pension reform, higher education and transportation.

McDonnell (R), unveiling his first state budget, proposed saving nearly $1 billion in a variety of ways, including withholding inflation increases for Medicaid and K-12 education, making state agencies more efficient and closing an aging prison.

He did not propose higher taxes, but he did recommended collecting $22 million in higher Department of Motor Vehicles fees, restaurant inspections and increased employer payments to the unemployment compensation trust fund.

In his annual speech to the General Assembly’s money committees, McDonnell told legislators that although revenue continues to grow, Virginia needs to be vigilant as it begins to recover from the worst recession since the Great Depression.

McDonnell, one of the nation’s most popular governors and a possible vice presidential contender, hopes to use his two-year budget to reshape Virginia’s government and leave a lasting mark on the state.

“We should not subscribe to the theory that government can only get better if it gets bigger,’’ McDonnell told a room of legislators, lobbyists and state employees. “I believe that government must get more focused and effective.”

The General Assembly will consider his budget recommendations when it returns for its annual legislative session Jan. 11. Legislators have the power to completely overhaul or ignore his $85 billion, 483-page plan.

McDonnell’s chances of getting his plan passed have improved because Republicans control the House and split the Senate with Democrats, with Lt. Gov. Bill Bolling (R) having the power to break tie votes. Democrats said they will challenge Bolling’s authority to vote on the budget.

In Northern Virginia, officials cheered the restoration of $25 million of a $120 million cut over two years in aid to localities but worried about a $65 million reduction in funds to woo school employees in a competitive, expensive market. “It’s a huge hit to all of Northern Virginia,” Del. David L. Englin (D-Alexandria) said.

McDonnell’s 60-minute speech touched so lightly on his proposed cuts that some were confused about how he would pay for it all.

“As I walked out of the room, I got grabbed by a number of people who said, ‘Where are the cuts?’ ’’ said Michael Cassidy, president of the Commonwealth Institute for Fiscal Analysis.

McDonnell made his deepest cuts in Medicaid, saving $259 million by not adjusting hospital payments for inflation. But the budget does not cut Medicaid provider rates, as some had feared.

The governor wants to add $110 million to ease clogged roads by boosting the portion of the sales tax spent on transportation. Democrats say that will take money away from education and other core services, but Republicans praised the approach.

“The governor has been a great ally in the fight for common-sense fiscal solutions, low taxes and budgetary prudence for many years,” House Speaker William J. Howell (R-Stafford) said.

After his speech, McDonnell told reporters that Democrats who argue the state cannot afford to shift money to transportation just want to raise taxes. “They don’t have the courage to tell people what we can afford and can’t afford,’’ he said.

McDonnell proposes an increase of $438 million for K-12 education as he looks to make good on a campaign promise to boost classroom spending. Of that, however, $342 million would go to replenish the teacher retirement system.

He also wants to withhold inflation adjustments for any non-teaching expenses associated with schools, ranging from secretarial salaries to utility bills, for a savings of $109 million. And he is proposing $108 million less than what was asked for the Standards of Quality, state-mandated minimum objectives for public schools.

“There is obviously inflation, and to say there isn’t reduces funding,’’ said Robley Jones, a spokesman for the Virginia Education Association.

The budget calls for an $81 million cut to pre-kindergarten programs — a top priority of McDonnell’s predecessor, Democrat Timothy M. Kaine — but state officials said that they had merely corrected faulty enrollment projections and that there would, in fact, be more money for pre-K.

The two-year budget, which begins July 2012, will be the largest spending plan in Virginia history, growing by about $7 billion. The governor’s staff noted that the general fund — the part of the budget that the state controls — has returned to 2007 levels.

The increase in the other part of the budget is attributed to revenue growth, an expected boost in federally mandated programs such as Medicaid, and more money from fees and colleges and universities.

McDonnell proposes setting aside $50 million to offset future cuts in federal aid as he looks to send a message to the nation’s three bond-rating agencies that they should keep the state’s stellar credit rating. He also wants to double the amount in the state’s rainy day fund to $600 million.

McDonnell would continue the state’s hiring freeze and reduce the 103,000-employee state workforce by less than 250, primarily by closing the Mecklenburg Correctional Center. He also proposes spending $77 million on a 3 percent bonus for state employees, but only if the employees can come up with ideas that would save $160 million.

In the past week, McDonnell has rolled out some of his spending proposals, including putting $2.2 billion into the retirement system for state and local employees, with about $1 billion of it paid for by localities. The amount includes the first two years of repayment of $620 million borrowed from the retirement system in recent years to close a budget shortfall.

McDonnell recommended spending $200 million on colleges and universities, pursuing his goal of creating 100,000 college degrees, and $100 million for economic development.