A quick analogy to highlight how ridiculous Republicans are being: imagine Romney won the presidency in 2012, Republicans gained control of the Senate, but lost House control to Democrats. Then imagine that instead of passing a budget or a continuing resolution, Democrats in the House (where spending bills have to originate) say they will let the gov't shut down unless the Senate and Romney agree to very strict gun control policy. That would be ridiculous. What's beyond ridiculous and a lot more dangerous is threatening to not raise the debt ceiling while advocating the same policy.
And that brings me to a point Matt Yglesias made today in regard to negotiations (I'm too lazy to link to his post. If your interested go to my twitter page.) He says that Dems and Obama shouldn't just sit back and wait for Republicans to cave and inevitably pass a "clean" CR, meaning it contains nothing about defunding or delaying Obamacare. He thinks their stance should be to also raise the debt ceiling, or actually, to get rid of the debt ceiling all together since it doesn't really serve any good purpose. I certainly agree with that as policy and as a negotiating tactic.
If I were Democrats and Obama I would think about going further and telling Republicans that I won't support a CR that doesn't get rid of the sequester cuts that were implemented as part of these same negotiations (or really, hostage taking) last year. Democrats don't like the sequester cuts because they hurt important programs they care about. Republicans also don't like the sequester cuts because they hurt important programs they care about. That was the point of the sequester, to force both parties to come to an agreement so that they could avoid something no one wanted. That didn't work and both parties seem to have rationalized maintaining the cuts. But even if Democrats aren't serious about getting rid of the sequester cuts I think it might not be a bad negotiating strategy.
Say Obama comes out in a speech talking about how bad this shutdown is and trying to convince everyone to blame Republicans for it and lays out what he wants as part of a negotiating tactic. He says at the very least he wants a "clean" CR. There will be absolutely no deal without that. The second thing he wants is what Matt says, a raise of the debt ceiling and an abolishment of it forever so that we don't default on our debt and create big economic problems. And the last thing he wants is to remove the sequester cuts from the CR because they are hurting the economy and important gov't programs.
If Obama were to spend the first round of negotiations pushing really hard for all of those things Republicans likely wouldn't budge at all and would likely try to get the press to blame him for asking for too much, thus extending the shutdown. The press may even play along and cast Obama as the main person to blame. Obama could then go back to the negotiating table and say that he'll accept a "clean" CR and debt ceiling raise but not the sequester cuts so that they could end the shutdown. Then Obama could say he's the one making concessions for the good of the country. And if Republicans don't agree to his concessions, he could try to shift the blame to them.
The problem with trying to move the debate to the left by demanding more than you would actually agree to in the end is that you have to convince Republicans that you are making a legitimate demand and you have to appear to be willing to hold out until you get it. I'm not sure Obama can convince Republicans of those things. And I'm not sure how willing they would be to getting rid of the debt ceiling once and for all. They were successful last year in using it to get something they wanted. So they would probably view getting rid of it as a concession instead of just a thing we as a country are obligated to do. All of these problems are why I only say this negotiating strategy should be considered. I'm not sure it would work. But it's at least worth thinking about.