One issue that keeps coming up in government shutdown talks is the idea of the GOP retreating to the "Vitter amendment" as a more moderate proposal than these efforts to defund Obamacare. To understand the merits of this proposal, you have to understand the merits of the Vitter amendment, which can be listed very briefly, as there are no benefits.
However, the rise of the Vitter amendment itself is a fascinating tale of the conservative media echo chamber.
It all goes back to an amendment to the Affordable Care Act spearheaded by Chuck Grassley. This was supposed to be a poison-pill measure that would force congressional staff to obtain their health insurance on Affordable Care Act exchanges. Grassley, because he's incredibly ill-informed, had gotten it into his head that Democrats would reject this idea out of hand. But Democrats genuinely think that health insurance exchanges are a good idea and were happy to sign on to this piece of legislative trolling. I would add that it's actually a doubly good idea to do this, because public officials are unusually attentive to the quality of public services that public officials actually use. That's why sequestration's impact on air travel was addressed much more adroitly than its impact on preschool for poor kids.
But there's a nuance here. The way most people—including congressional staffers—get health care is that their employer partially pays for it. The way the exchanges work is that the government provides subsidies so that people who don't currently get employer-provided insurance can afford to buy it. The Grassley amendment, on one reading, would create an anomalous situation where not only would congressional staff have to buy insurance on the exchanges they'd be taking a large de facto pay cut. That's because they'd be losing a valuable perk (employer-provided insurance) and given nothing in exchange for it. That doesn't really make sense as public policy, and certainly Grassley's intention wasn't to enact an across the board cut in congressional staff pay. He was just trolling. At any rate, the Office of Personnel Management stepped in and said they did not interpret the Grassley amendment in this way. Instead they read it as authorizing the government to redirect money currently spent on buying health insurance for congressional staff to subsidizing the purchase of insurance on Obamacare exchanges. Thus, congressional staff will participate in the exchanges and the exchange process but won't end up taking a pay cut.
Somehow the conservative press convinced itself that this constituted a "special congressional exemption" from Obamacare or from the individual mandate. At this point David Vitter—whether out of stupidity or what I can't quite say—took up this banner and has been sponsoring legislation that would overrule the OPM and force the perverse reading of the Grassley amendment onto the government.
Bringing the Vitter amendment into the government shutdown fight serves one very important purpose for cynical Republicans. Democrats do not like the Vitter amendment (because it's dumb), and yet if the government shuts down over a Vitter amendment dispute, that would arguably make the Democrats look bad rather than the Republicans. If GOP leaders can persuade their crazy base that this Vitter amendment fight is important, that would allow the leadership to extricate itself from the untenable situation it's currently in. That said, the problem for Republicans here is that the Vitter amendment is really dumb. It's entirely possible that if they pick the fight on these grounds, Democrats will have to cave. At which point congressional Republicans will have succeeded in cutting their staff's pay and not much else. Not anything else, in fact. The implementation of Obamacare won't be impacted at all even a tiny little bit.