In short, the suit claims that paying these subsidies out of an account that has not been appropriated by Congress is a breach of the separation of powers, and by passes Congress’ authority to hold the purse strings.
The anti-ACA activists see this as a means to dismantle the Act in piecemeal fashion, whereas the supporters believe it nothing more than a partisan move to curry favor with a certain segment of the population.
From an objective view, the likely outcome of the suit will create some language changes in how the law is executed, but will have minimal impact on the intended delivery of service. The Supreme Court has already facilitated continuance of the law despite similar challenges, and it is unlikely to render a decision that would cripple the program. Love it or hate it, it’s here to stay.