WASHINGTON — Proclaiming a “once in a generation” opportunity, President Obama proposed a 10-year budget on Thursday that reflects his determination in the face of recession to invest trillions of dollars and his own political capital in reshaping the nation’s priorities.

Mr. Obama would overhaul health care, begin to arrest global warming, expand the federal role in education and shift more costs to some corporations and the wealthiest taxpayers.

In a veiled gibe at the Bush years, Mr. Obama said his budget broke “from a troubled past” and attributed the current economic maelstrom to “an era of profound irresponsibility that engulfed both private and public institutions from some of our largest companies’ executive suites to the seats of power in Washington, D.C.”

Without trimming his ambitious campaign promises, the president projects a budget for the 2010 fiscal year of nearly $3.6 trillion. He said he would shrink annual deficits, now at levels not seen in six decades, mostly through higher revenue from rich individuals and polluting industries, by reducing war costs and by assuming a rate of economic growth by 2010 that private forecasters and even some White House advisers consider overly rosy.