Democrats have accused Bush of seeking to cut taxes and spending on health care while projecting huge costs for Iraq.
Bush's budget would achieve nearly $100bn in savings over five years by lowering increases in Medicare, the health insurance programme for 43 million retirees and the disabled, and Medicaid - which provides health care to the poor.
The sum amounts to a decrease in many US domestic programmes after accounting for inflation, which is running at about 2.5 per cent.
Kent Conrad, the senate's budget committee chairman and a Democrat, said: "In real terms, Bush's plan is going to have very substantial cuts by the fifth year of this budget in all of the domestic priorities from education and health care to law enforcement and veterans.
"With Democrats in control, we will have different priorities."
Bush said on Saturday: "Controlling spending also requires us to address the unsustainable growth of entitlement programmes such as social security, Medicare, and Medicaid.
"Spending for these programmes is growing faster than inflation, faster than our economy, and faster than our ability to pay for it."
Some Democrats have expressed fears that the price tag for the war could end up being even higher than Bush has estimated.
Until now, the war chest had been filled in the formerly Republican-controlled congress through "supplemental" requests that go through less debate than the annual budget.
The arrival of the massive four-volume set of green budget books, which will cover the budget year that begins next October 1, will be followed by months of debate in Congress.
US taxpayers have spent $503bn for the "war on terror" since 2001, according to the non-partisan congressional budget office.