Either side could have stopped the shut down so how is one party or person responsible. It happened because neither side would budge, the side you believe was wrong is the one responsible.
That's empirically incorrect. Republicans voted for a bill that included funding for ObamaCare. Even though they didn't like it they knew that ObamaCare was a law that had been passed by the house and senate and sighed into law by the president and required funding. It was not one side or the other that was at fault, it was Ted Cruz and his minions.