With a deadline for raising the debt limit fast-approaching, House Speaker John A. Boehner (R-Ohio) has been telling colleagues in recent days that he will do whatever is necessary to avoid defaulting on the federal debt, including relying on House Democrats to help pass an extension, according to GOP aides familiar with the conversations. In a series of small group meetings held in his office suite off the rotunda of the U.S. Capitol, Boehner also has been telling colleagues that he will not permit a vote on a “clean” continuing resolution that does nothing about ending or delaying parts of the new federal health-care law. Relying on Democratic votes to pass a debt ceiling extension likely would infuriate some of the most conservative members of the House GOP conference.