WASHINGTON — Two years ago the departing chairman of the Joint Chiefs of Staff, Adm. Mike Mullen, declared that “the most significant threat to our national security is our debt.” After a decade in which the nation had chased Al Qaeda and invaded Iraq, Admiral Mullen was saying, in essence, that the biggest enemy was us.

Now that Congress and President Obama have slipped past the latest budget deadline with a bill that does little to address the country’s long-term debt issues — and by some measures might worsen them — the worries of the national security establishment have been reignited. Most pointedly, military and diplomatic experts wonder whether the United States is at risk of squandering its global influence.

“There’s a sense that we’ve been playing roulette with our position, and this deal does nothing to stop that,” Richard N. Haass, the president of Council on Foreign Relations, said in an interview. His coming book, “Foreign Policy Begins at Home,” is part of a wave of recent literature arguing that America’s reduced global ambitions are linked to its status as a debtor nation.

Vali Nasr, who will soon publish “The Dispensable Nation,” argues that the debt, among other economic woes, has allowed Mr. Obama and other Democrats to justify a retreat from global engagement. “It’s made it far easier to say ‘We can’t do more,’ ” said Mr. Nasr, the dean of the School of Advanced International Studies at Johns Hopkins University. “And without addressing the debt issues, it will be easier to make that argument for years to come.”