WASHINGTON — President Obama expressed confidence on Monday that he was right to defy House Republicans’ demands as the hours ticked away toward a government shutdown. Yet offsetting the bravado at the White House was fear of what October’s unfolding events could mean for the economy.

A day before uninsured Americans could begin signing up for coverage under the Affordable Care Act, the law that is the white-hot center of the political conflagration, Mr. Obama appeared self-assured but was nonetheless powerless to influence scores of uncompromising Republicans — many of them elected since he took office — who have bucked both their own party leaders and traditionally influential business groups. As he acknowledged, five years of work to prevent a second Depression and then spur a slow recovery was at risk of being undone, depending on how the month plays out.

Hope for a short-term deal to fund the domestic and military operations of government slipped away as a new fiscal year began Tuesday at 12:01 a.m., and a fight is inevitable as the president and Congressional Republicans seek agreement for a full-year budget. The biggest, most economically threatening showdown still threatens: By Oct. 17, Congress must raise the nation’s debt limit to pay for bills already incurred or provoke a globe-shaking default.