Tease, actually the US Senate was responsible since they refused to adopt the spending bill forwarded to them by the US House of Representatives. Nevertheless, the responsibility for the shutdown of the US government ultimately still rests with Obama since the Democrats are acting as his proxies. Obama, himself, set the stage by stating that he will not negotiate with the Republicans, which tends to be an impediment to compromise.
Obama has also gone on to say that after he gets what he wants from Congress in the way of a budget, that he would then be willing to have a "conversion" concerning the future of the Affordable Care Act (Obamacare). Well that's an absurdity. Why would Obama all of a sudden negotiate after he received everything he demanded? Not only that, but Obama already had 365 days (one budget cycle) to have that "conversation" with the Republicans, and he avoided making that a reality.
Furthermore, Obama has unilaterally made revisions to the Affordable Care Act, without the consent of the Congress. Obama has, on his own volition, changed the law, granted waivers, and delayed implementation of the Affordable Care Act. An abuse of Executive Authority since the President is limited to implementing the law as passed by Congress, not changing it. Yet Obama refuses to negotiate with the US House of Representatives, which is a law making body. Again, if Obama refuses to work with the US House of Representatives to legally fix what is broken with the Affordable Care Act, it is Obama who is shutting down the US government.