The concerns of American officials extend beyond the health of the European economy and the stability of global financial markets. Greece is a member of NATO, and its economic estrangement from other members of the alliance, which operates by consensus, has the potential to complicate American foreign policy at a time of rising tensions with Russia and turmoil in the Middle East.

The White House has made a point of noting in recent days that Greek stability is in the United States’ national security interest as well as in its economic interest.

“They’re worried, but they’re limited in what they can or should do,” said Doug Rediker, a visiting fellow at the Peterson Institute for International Economics and a former appointee of Mr. Obama’s to the I.M.F.’s executive board. “They have gone out of their way, both the White House and Treasury, to try and explain to all the European parties why coming to a deal is better than not coming to a deal, but they’ve been respectful of the fact that it is largely a European issue, and the vast majority of the funds that are at risk are European funds.”

The White House declined on Tuesday to comment publicly on any aspect of its response to Greece’s financial troubles, although a senior administration official said Mr. Obama had been heavily engaged on the matter. Mr. Lew has had more than 60 phone calls or meetings with European officials on the matter over the past six months, and both he and the president have raised it frequently with their foreign counterparts.

The United States has consistently argued that both Greece and its creditors must make sacrifices to preserve the currency union. Mr. Obama has backed European calls for Greece to expand economic reforms, including further cuts in public spending, but he warned in February that “you cannot keep on squeezing countries that are in the midst of depression.”