The current government shut down has nothing to do with the Affordable Healthcare Act. It has everything to do with Constitutional Division of Powers.
According to the Constitution, spending bills must originate in the House of Representatives. The House of Representatives decides on whether we should spend money on a particular government activity. The Senate is responsible for Authorizing the money to be spent.
This is a checks and balance built into our Constitution. It requires the House of Representatives to fund a government activity. It requires the Senate to Authorize the spending of money.