WASHINGTON — With the deal reached Sunday night, the United States has a good chance of escaping the debt limit showdown with its credit rating intact.

The United States government may not be so lucky with its reputation.

Even before negotiations went down to the wire on Sunday night, the bitterness, division and dysfunction that resounded around the world in recent weeks as the United States veered toward default did more than just fuel a perception that Washington is approaching Japan-like levels of political gridlock. Among foreign leaders and in global markets, the political histrionics have eroded America’s already diminishing aura as the world’s economic haven and the sole country with the power to lead the rest of the world out of financial crisis and recession.

It has chipped away at the global authority of President Obama, who was celebrated abroad when he came to office as a man who would end an era of American unilateralism. Now the topic of discussion in other capitals is whether the Age of Obama is giving way to an Age of Austerity, one that will inevitably reduce America’s influence internationally.

Mr. Obama has all but acknowledged as much in recent weeks, as he paired his decision to withdraw the “surge” troops from Afghanistan by next September with a repeat of his declaration that “it is time to focus on nation building here at home.” His decision to commit few new American financial resources to supporting the Arab Spring and his insistence that NATO allies must bear the brunt of operations in Libya were deliberate reminders that times have changed, and that America can no longer afford either new Marshall Plans or new wars.