Committees have near absolute control over all bills introduced in Congress. Most controversial bills are killed in these committees. In theory, it is already possible. A majority of senators or representatives can suspend normal voting procedures. A bill is simply put in writing, including a header that suspends any rules against petition voting.
Members vote by signing the bill.
The president has always had this power and could at least attempt to use it. An independent candidate for U.S. Senate must collect 36,051 petition signatures to qualify for the general election ballot. A vote in the primary should be equivalent to a petition signature. Contrary to popular opinion, we have many capable and honest representatives in Congress. The problem isn't so much who we send to Congress, but how Congress operates.