In Trump’s own words, the government shutdown is the president's responsibility — which means he is to blame. See for yourself:

2013: Trump repeatedly said a government shutdown was the president’s responsibility.

Trump: “They talk about the government shutdown, they're going to be talking about the president of the United States — who was the president at that time? … I really think the pressure is on the president.” 

Trump: “You have to get everybody in a room. You have to be a leader. The president has to lead.”

2011: Trump said the president would be blamed for a government shutdown.

Trump: “If there would be a shutdown, I think it would be a tremendously negative mark on the President of the United States.”

Trump: “My sense is that people are far angrier at the President than they are at Congress re the shutdown—an interesting turn!”