Boehner made his closing arguments at the party’s annual mid-January retreat in Williamsburg, Va., where reporters and other outsiders were mostly kept at bay.

A daylong session began with Boehner explaining what he saw as the financial and political ‘‘facts about the debt ceiling,’’ a participant said. Next up were his top lieutenants, to amplify his remarks and discuss possible options: House Majority Leader Eric Cantor of Virginia, House Ways and Means Committee Chairman Dave Camp of Michigan and House Budget Committee Chairman Paul Ryan of Wisconsin, the party’s vice presidential nominee last year.

They left no doubt of the party hierarchy’s allegiance to Boehner.

House Republicans agreed to postpone the debt-ceiling showdown for three months. That will let Congress deal first with two less dire issues in which Republicans feel they have more leverage: the scheduled start of big, across-the-board spending cuts and the need to approve funds to keep the government running another year.

‘‘Everybody took a hard look at it and said we can’t govern from the House of Representatives,’’ said Republican strategist Mike McKenna. Rather than confront Obama ‘‘army to army,’’ McKenna said, Republicans decided to ‘‘do a little more sniper action.’’

It’s unclear how long the calm will last.

The 151 House Republicans who voted against the Boehner-backed fiscal cliff deal on Jan. 1 ‘‘will get tired of the incrementalism of the debt ceiling’’ issue, McKenna predicted. For now, however, he joins others in saluting Boehner’s breakthrough.