WASHINGTON — President Trump plans to unveil on Tuesday a $4.1 trillion budget for 2018 that would cut deeply into programs for the poor, from health care and food stamps to student loans and disability payments, laying out an austere vision for reordering the nation’s priorities.

The document, grandly titled “A New Foundation for American Greatness,” encapsulates much of the “America first” message that powered Mr. Trump’s campaign. It calls for an increase in military spending of 10 percent and spending more than $2.6 billion for border security — including $1.6 billion to begin work on a wall on the border with Mexico — as well as huge tax reductions and an improbable promise of 3 percent economic growth.

The wildly optimistic projections balance Mr. Trump’s budget, at least on paper, even though the proposal makes no changes to Social Security’s retirement program or Medicare, the two largest drivers of the nation’s debt.

To compensate, the package contains deep cuts in entitlement programs that would hit hardest many of the economically strained voters who propelled the president into office. Over the next decade, it calls for slashing more than $800 billion from Medicaid, the federal health program for the poor, while slicing $192 billion from nutritional assistance and $272 billion over all from welfare programs. And domestic programs outside of military and homeland security whose budgets are determined annually by Congress would also take a hit, their funding falling by $57 billion, or 10.6 percent.