Civil officials and judges can be impeached, not congressmen.
Senator William Blount of Tennessee was impeached by the House of Representatives in 1797. The Senate expelled Blount so the impeachment trial did not go forward.
If Boehner was impeached it would take every Republican in the Senate, including the RINOs to vote against him plus they would need 13 Democrats in order to get to the required 67 votes needed to remove him from office.
The original poster’s premise that it was a close election is flawed. Boehner received 216 votes to Pelosi’s 164 and 26 votes were cast for other candidates. The most any single alternative conservative candidate got was 12 votes for Representative Daniel Webster of Florida.