"I believe votes would have been there for the THUD bill, but we had some 50 amendments yet to consider on that bill, and considering everything else we've got on this week, [we] decided that finishing that bill in September was the right thing to do," Boehner said during a news conference.
"I had full confidence that the votes would have been there to pass that bill," he continued.
The House's decision to pull the Transportation and Housing measure touched off a round of internal finger-pointing as Rogers criticized Republicans for opposing a bill that included budget cuts they said previously they wanted.
The House's THUD measure, which drew a veto threat from President Obama, cuts $7 billion from the Transportation and Housing departments' 2013 budgets. The measure includes a 21 percent reduction to Amtrak's appropriations and completely eliminates high-speed rail funding, which had been a priority of the Obama administration.
The bill also cuts $1.3 billion from the Housing and Urban Development's Community Development Block Grant program.
The Senate was unsuccessful in its attempt on Thursday to pass its own version of the Transportation and Housing bill that would have spent $10 billion more than the House on the departments. A vote to close debate on the measure failed to reach the 60-vote threshold to advance the legislation on Thursday.
-Erik Wasson contributed to this report.