That would just end in a situation even worse than now - such a policy requires a government in the continental European parliamentary form to make sure the government always has a parliamentary backing.
No, actually it would be far superior. We should strictly limit the power of the Federal government to what was actually intended by the Founders instead of using the Commerce Clause as a loophole. Devolve everything else to the several states.
We tried that. It was called the Articles of Confederation[0]. It was an unmitigated disaster, and the reason we have our current Constitution with power actually consolidated under a Federal government.