They have an open constitutional convention right now located at the SCOTUS and every other unelected area of the Federal Government, from the IRS to the EPA.
Regardless of the amendments proposed they must still be ratified by a super majority of State Legislatures. The last I checked they where overwhelmingly Republican and much closer to the average American than your every day Supreme Court Justice of Special Investigator at the IRS.
Article five is the last resort short of open rebellion to reign in an abusive power hungry National Government.
There is absolutely nothing to lose, and everything to gain from an Article V convention to propose amendments.
I get that. I do. But I'm pretty sure the whole Article V thing will NOT go precisely as current supporters think it will, especially once the left realizes they better get on board, and get their interests on board.