WASHINGTON — The Chinese dissident Chen Guangcheng’s abrupt reversal and plea for protection from the United States has deepened a diplomatic crisis and exposed the Obama administration to withering criticism that its diplomats miscalculated when they negotiated his departure from the American Embassy in Beijing.

Mr. Chen’s request for help from Secretary of State Hillary Rodham Clinton — repeated in an urgent telephone call played on speaker during an emergency Congressional hearing on Thursday — frayed a fragile deal American officials negotiated a day before the start of high-level talks between China and the United States.

Mr. Chen has now proposed that he and his family be allowed to visit the United States temporarily, rather than request permanent asylum there, according to an American lawyer, Jerome A. Cohen, who has advised him this week. The proposal, Mr. Cohen said, could be a face-saving solution for China, defusing a situation that threatens relations between the two countries.

As the State Department tried frantically to reassess the options for Mr. Chen, who is now at a hospital in Beijing being treated for an injured foot, senior American officials privately acknowledged missteps in the handling of the case. The United States failed to guarantee access to Mr. Chen at the hospital, they said, leaving him isolated and fearful that China would renege on its pledge not to harass him and to allow him to resume his legal studies.