Well, it's been more than a week. And everyone is speculating when it will end. Only a true anarchist would want it to continue much longer, but how and when it will end is not so clear. For that is what we are heading for without a functioning government, anarchy.
Those who look a bit further into the future see the upcoming borrowing ceiling as a more serious issue as the government will start to run out of money by the middle of October. By the end of the month the government would be out of all tricks and resources and would need to either default or selectively pay the bills. As selective paying of bills a minefield in itself, probably the course of action will be to not pay anything. This would, as many have pointed out, have serious repercussions for the US reputation and credit worthiness. But, more importantly the confidence in the soundness of a US bond will be shattered. US debt is considered so secure that the interest rate on it is considered the standard of risk free return on investment. All other investments are compared to US debt when deciding whether the risk/reward is worth the premium of return above that which could be had from parking the funds in US debt. Thus the entire worldwide financial planning system would be shaken. Still, a few missed payments may not have such a dramatic effect if the government is funded shortly thereafter and any who suffered losses were made whole by receiving their payments with some extra interest.
But more seriously, and I have to give credit to the President that he sees this, is that the threat and action of shutting down the government is being used to try to create yet another way to legislate, outside of the standard Constitutional process. "Obamancare", the law that opponents want to overturn was passed by the standard lawmaking process. Those who supported and opposed the legislation put up their arguments, their influence, and their votes. In spite of all opposition, the bill passed and became law in the United States. Opponents, not happy to have lost by the Constitutional lawmaking process see shutting down the government as a mechanism to get their way after all. If they were to succeed this would enshrine a new form of coercion as a mechanism to enact or repeal laws outside the standard Constitutional framework. Ultimately, the President has to stand firm to prevent this radical alteration in our lawmaking process