Third parties are a sucker's game. The only ways to affect change are either to control both the Hill and the White House, or get a veto-proof majority. Re-taking the White House is a likely outcome at this point, IMO.
There were 52 republican congressmen who voted to not fund Obama's Amnesty in DHS. This was not a government shut down not shutting down DHS just the 15% of DHS that would help Obama's Illegal Amnesty.
Saying stuff that isn't true is also not helpful. The "Deferred Action for Parents of Americans and Lawful Permanent Residents" applications will be processed by Citizenship and Immigration Services, if (repeat if) the E.O. survives the legal challenges. CIS is the only DHS bureau funded exclusively by user fees. CIS is not appropriated and if Congress de-funds DHS, CIS continues to adjudicate petitions as normal. It did not shut down in 2013 during the last budget impasse. It will not shut down if another budget lapse occurs.
When you read that only a small part of DHS would be inoperable, that refers to the distinction between "essential" and "non-essential" staff. Essential staff in law enforcement jobs (border patrol, etc.) the Coast Guard, Secret Service, and others would continue to work for no salary until a budget is passed. Non-essential staff can be anything from attorneys, to human resources and payroll clerks, to admin staff overseeing IT contracts. The U.S. Antideficiency Act makes it illegal for them to work for free. They'd be furloughed in the short run, but it ends up costing more in the long run because of all the additional work and overtime needed to catch up for the days and weeks lost.