Rep. Rob Bishop, R-Utah, panned Matheson's idea calling it "cute" and a message with little substance behind it.
"Just physically being in here doesn't mean squat," he said just off of the House floor on Tuesday. "And just because I'm physically not here doesn't mean people are not working on this issue."
Bishop was instrumental in changing the House schedule to allow members to spend more time in their districts after the Republicans took control in 2011.
He said the district work periods, often called recesses, have allowed him to work on issues directly with people who are affected by them. As an example, he said during last week's recess, he met with people at Hill Air Force Base to discuss the potential impacts of the across-the-board budget cuts that will kick in on Friday unless Congress takes action.
Matheson argues serious fiscal issues like the so-called sequester are the very reason members of Congress need to spend more time in Washington. He said last week that he heard from people who want members of Congress in the same room hashing out a compromise.
"Being in Washington is a precursor to getting something done," he said in an interview. "When we are on recess for a week, there is no way it can happen."