President Obama and House Speaker John A. Boehner moved close to agreement Monday on a plan to avert the year-end “fiscal cliff,” but they had yet to clear several critical hurdles, including winning the support of wary House Republicans.

Administration officials and aides to Boehner declined to comment publicly on the talks. But people in both parties said they continued to make progress as Obama laid out a counteroffer that reduces the amount of new taxes he is demanding to $1.2 trillion over the next decade and concedes a key Republican demand: applying a less-generous measure of inflation to several government programs, including Social Security.

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