They don't vote on 'every penny'. It's not quite that micromanaged. Morwen already said it pretty clearly, but I'll repeat it in another way.
Congress has to vote to continue funding for the next year of Federal services. One side has refused to pass any bill that includes Obamacare in it. The other side has refused to pass any bill that does NOT include Obamacare. They could pass the other things separately and keep arguing over Obamacare, but if everything else is paid and there's no crisis, the Democrats would not have any leverage to push the issue and the Republicans could safely ignore them - so the Democrats refuse to pass any bill that doesn't include what they want. The only individual things that have been passed are a few bits and pieces like continuing to pay military salaries and such. Small concessions that lessen the impact of the shutdown.
Don't make the mistake of assuming the shutdown is unintentional, or a side effect. It is very much intended, and it is a powerful bargaining chip and force of political leverage. "If you don't do what we want, everything shuts down." is the threat and reality being faced. If either side agrees to make concessions and allow funding to pass to stop the shutdown, they lose.
This is a very binary debate right now. Either Obamacare does or does not get funded with everything else. There is no in between. The most likely result of this is that one or both parties will lose cohesion and members will start voting for the other side in fear of not being re-elected. As the American people grow angrier, they will stop caring about the politics and demand the government get back to work. That means Congress members from one or both sides have to give up 'toeing the party line' or risk losing their careers.
Democrats may break from the DP and vote for the other side or a compromise bill that does not fund Obamacare, because they want to stay in office. The American people are the ones who re-elect them, and the American people will eventually demand an end to the stalemate.
Republicans may break from the GOP and vote for the other side or a compromise bill that supports Obamacare, because they want to stay in office. The American people are the ones who re-elect them, and the American people will eventually demand an end to the stalemate.
Tea Party (extremist Republicans) members will probably not break ranks and may gain or lose popularity depending on which side breaks down first. This is one of their "hail mary" plays, and will be a strong deciding factor in where the Tea Party movement goes from here.