Republicans see themselves and would like voters to see them as the grown-up party, sober and responsible. Democrats always caricature Republicans as anarchists who want to eliminate government entirely. A futile fight to defund Obamacare that touched off a government shutdown crisis would reinforce the Democrats' indictment and provide a wobbly Obama with the opportunity to change the subject from his own failures to the petulance and recklessness of Republicans.
In a shutdown show down, Republicans are certain to lose the battle for public opinion. When the question is: "Whose fault is it that government offices are closed?" the public will be more inclined to blame the anti-government party. The press, of course, will side with Democrats. The public opposes Obamacare, but it does not favor shutting down the government in order to thwart it. If Republicans threaten to pull down the house over it, the public will be more likely to perceive it as a personal vendetta against Obama than as a principled policy stand.
Obamacare may be the best thing to happen to the Republican Party's fortunes. When voters see 1) that their premiums rising; 2) that wait times to see a doctor are increasing; 3) that they are forced to buy insurance they don't want or pay a fine; 4) they find that their spouses are no longer covered by their employers' plans; 5) learn that they cannot, as promised, keep the plan they were happy with, and more, they will not blame Republicans. Nor will Obama be able to blame this one on Bush. Republicans who focus on the small number of Americans who will get subsidies under Obamacare are missing the bigger picture, which will be widespread discontent.
It may well represent the best political opportunity for Republicans in more than a decade. If they take the Senate in 2014 and the presidency in 2016, it will not be too late to repeal Obamacare. At the rate it's going, it probably won't even be fully operational by then. But Republicans will have to cease their fratricide to take advantage of it.