Just realized I made a bit of a mistake in the above post. Technically, they're trying to use congress's control of the budget to block all funding that would previously have been allocated to implementing the ACA (aka obamacare.) While this wouldn't be a true repeal, it'd effectively be the same thing since the law would become impossible to implement any further without funding. The true repeal would come (presumably) at a later date.
For anyone who isn't really familiar with our systems, it should be noted that this budget appropriation thing is normally considered routine, since congress would have already modified whatever programs they wanted to beforehand. This is happening because the law they don't like is already passed, and doesn't have the votes to be repealed, (and believe me, it's been tried. Something like 43 times iirc) so one house is hanging the budget up as an attempt to get around the normal system.
Yeah, it's really complicated. My understanding really isn't that great, so if anyone sees more mistakes, please point them out.
For what it's worth, while the shutdown is bad, it's not going to cause any significant longterm effects. The debt ceiling needs to be raised before the 17th, so it's expected to be resolved before then. Boehner (the current speaker of the house) has made it clear he's not willing to let it go that far. Probably what happens is Boehner finally caves at the last minute, then uses this as the prime example for the whole "Obama is never willing to negotiate" narrative he's been pushing. President Obama gets to go on about how the evil Republicans took away all the government workers' pay for a couple weeks because they don't want poor starving children to have healthcare, etc. It's almost a win/win for both sides, since they get something new to get their base all outraged about.