There is no way to assert the proper role of Congress (let alone the proper role of the Republican party) against the permanent Democratic bureaucracy without working a serious, full-time schedule. Part-timers can't accomplish that much under the circumstances. This is one of those situations in which the Framers' wisdom, which was almost always sound in its day, truly doesn't apply anymore. Romantic notions of citizen government are self-defeating at this point.
Democrat notions of government will be worse.
It is only that the scope of the Federal Government has been expanded far beyond what the framers could have envisioned that makes a part time legislature infeasible.
If they want to be lazy, shrink the government to back within its Constitutional parameters.
Heck, they could even (for once) vote themselves a raise after such, and I might not object.