Mr. Clinton and Mr. Gingrich could spend hours in policy discussions. In the 1980s, President Ronald Reagan and Speaker Thomas P. O’Neill Jr. shared evening drinks and Irish storytelling. So far, at least, Mr. Obama and Mr. Boehner have spent virtually no time together and have made little effort to forge a bond. Aides said they could not recall a single one-on-one meeting or substantive phone call.

“I’m surprised Obama hasn’t done more to develop a relationship with Boehner,” said Steve Elmendorf, a House Democratic official during the 1990s. “They both like to play golf. I’d invite him four times a year to play golf. You may not get a lot of big things done, but there’s going to be the debt limit, some foreign policy thing. There’s going to be times when you’re going to need him.”

As a result, it may be hard for Mr. Obama to reach out to the emboldened House Republicans. “This is the price President Obama is going to pay for a while for completely ignoring the Republican leadership in the House and Senate in the first two years,” said Rich Galen, a Republican strategist who advised Mr. Gingrich.