While nobody can predict how long this impasse will last, personally, I think it will be resolved before Oct 17, 2013. Oct 17 is when the U.S. will hit its debt ceiling and the country will be so low on cash that it will not be able to make payments on its existing debt, according to Treasury Secretary Jacob Lew.
The U.S. defaulting on its debt is such an unthinkable failure that I pray our congressmen can resolve their petty political difference before then. If the U.S. defaults, then government services will be slashed, interest rates will rise, the financial market will panic and our debt will be downgraded (again). The price of gold will climb - even if the U.S. needs to liquidate its gold assets to make its interest payments. In the long-term, international banks and governments may even considering using the Euro as the world's reserve currency. All of that would be a huge blow to an already slow U.S. economy.