The House conservatives who refused to keep the government open without kneecapping ObamaCare seem to believe, now that the government has shut down, they can win the public opinion fight and force Democrats to back down.

But to make the case that their actions and demands were reasonable, Republicans need arguments that are remotely plausible. Instead, they are heading into battle with claims that I would call paper-thin, were that not a grave insult to paper. Here are the five legs on which the Republican position can't stand.

1. Obama won't negotiate

Speaker Boehner embraced this argument in a web video with the tag line, "Why is the Obama administration willing to negotiate with Putin on Syria... but not with Congress to address Washington's spending problem?" That's a disingenuous reading of the situation. Washington is at an impasse because Republicans have repeatedly snubbed Obama's offer for a budget compromise that pairs a stingier Social Security cost-of-living formula with corporate tax increases. Republicans refused to negotiate over taxes. They have continually demanded that Democrats scrap President Obama's biggest legislative achievement in exchange for simply keeping the government operating. Of course Obama won't negotiate over that. Otherwise, Obama has proved quite willing to negotiate on all aspects of the budget. It's Republicans who have refused offer to any concession of any sort.

2. Republicans have already compromised

Sen. Ted Cruz tried this one during his Sunday Meet The Press appearance: "My position in this fight was we should defund [ObamaCare], which is different from repeal. And even now what the House of Representatives has done is a step removed from defunding. It's delaying it. Now that's the essence of a compromise." No, the essence of compromise is when each party gives up something. Republicans aren't proposing to give up anything. They're just demanding a little bit less than before. Meanwhile, Democrats aren't asking for any trophies. Keeping the government open and raising the debt limit aren't ideological prizes, but basic housekeeping.

3. Republicans are just demanding what the people want

Republicans are nominally correct in saying that polling shows a lack of majority support for ObamaCare. But you don't have to look much deeper in the data to see that doesn't translate into majority support for threatening government shutdown to defund or delay ObamaCare. Multiple polls show widespread opposition to the Republican strategy linking the funding of government operations to stopping ObamaCare. Sixty-three percent of the electorate says Congress should "provide the funding to keep the government operating and deal with the health care issue separately." Sixty percent say avoiding a shutdown is more important than "cutting the funds" to implement ObamaCare. Four in five people say threatening shutdown is "not an acceptable way to negotiate." Even if you take the threat of shutdown out of the question, the Republican position still polls poorly. Only 38 percent support the view that "funding for the 2010 health care law must be cut off as part of any budget agreement," with 50 percent opposed. Furthermore, the notion of widespread opposition to ObamaCare on conservative grounds is also misplaced. As CNN's polling has long showed, while support for ObamaCare is below 50 percent, about 10 to 15 percent of that opposition says the program is "not liberal enough." Support for the Republican view that ObamaCare is "too liberal" is only in the mid-to-upper 30s.

4. Harry Reid is the one who shut down the government

On Meet the Press, Sen. Cruz claimed: "[Sen. Majority Leader Harry Reid's] position is 100 percent of ObamaCare must be funded in all instances, and, other than that, he's going to shut the government down." To translate, Sen. Reid's position is programs that Congress has already established by law should be properly funded. Reid is not the one who brought these issues together. House Republicans are the ones who made the decision to repeatedly link the suffocation of ObamaCare to legislation that would keep the government open; that was the threat, a threat on which Republicans have now followed through.

5. Since Obama is delaying ObamaCare for his friends, he should for everyone else

Also on this Sunday's Meet The Press, GOP Rep. Raul Labrador tried to make the case for a one-year delay of the entire Affordable Care Act program because there have been delays regarding certain provisions: "The president has already delayed it for big businesses. They have delayed it for all his friends … all we're asking for in the House of Representatives is for a one-year delay. Just like the unions are asking for a one-year delay." That doesn't make any sense. If Obama's objective was to go easy on his friends and save them from a bureaucratic disaster, don't you think the unions that supported his re-election would be getting help before the big businesses that didn't?

The real story is that the delay for the mandate on employers with 50 or more workers was to give extra time to resolve a specific issue that arose: a concern that the paperwork was going to be unnecessarily burdensome on the vast majority of businesses that already provide insurance. So a delay was issued to provide the time to resolve that specific matter. Soon after, certain unions tried to use the employer mandate delay, not to get a similar temporary delay, but to permanently change a rule that denies ObamaCare subsidies to a particular kind of employer-based insurance utilized by union members. Obama told his union friends, no, there's no legal basis for giving you those subsidies. The president is not doling out special favors. Nor does he consider the need for a few delays to resolve discrete issues to be cause for junking the entire law. In turn, these unions accepted the president's answer and continue to support ObamaCare. They did not throw a temper tantrum and call for a general strike that would grind the entire economy to a halt.

Perhaps Republicans can take a lesson from that.