In theory, that isn't too far from the system we have. The President was never meant to have so much authority, and Congress already requires a 2/3 majority in order to make certain kinds of decisions, including overruling a presidential veto.
There was some debate whether or not to remove the rule requiring a 60% vote to end filibusters in the Senate. Because this rule still stands, most laws cannot pass without 60 Senators' votes. Budget reconciliation bills, however, can be advanced with only a simple majority of the Senate. Though this is not a recent rules change, much recent legislation has gone through the reconciliation process to avoid the supermajority requirement.
