The US defaulting on its debts has both internal and external effects. The total of US government debt is over $ 16.9 trillion. (US Debt Clock) Of that debt, $ 4.8 trillion is owned by governmental agencies. This includes agencies such as the social security (holds over $2.5 trillion dollars). Of the public debt, foreign investors own $5.7 trillion. Keep in mind this is just the actual government debt; effects of a default would be much bigger. The US reached its debt ceiling in 2012. The US constitution - 14th Amendment, Section 4 - directly forbids the government from defaulting on its debt. Thus to cope with the debt ceiling being reached the government has been taking extraordinary measures in order to pay their debts (for instance suspending investments on individual pension funds). When these measures are exhausted, the government will not bring on a global economic collapse as they default on all their bonds. They will just be forced to balance the economy - to match their spending with their collected revenue. This is a very different issue (still with its problems) to a full default.
What is important is that a full default is likely to not happen. The brinksmanship between the rogue Republicans