No. The fact that the shutdown and the debt-limit standoff have happened in the same month this year is coincidental.
A so-called shutdown involves closing parts of the federal government when Congress fails to pass spending bills to fund them. It doesn't matter whether the government is in deficit or in surplus 鈥� so long as Congress has agreed to fund federal programs either for the entire fiscal year (via a budget) or for a shorter amount of time (via a continuing resolution), there will be no shutdown.
This is what happened on Oct. 1. Congress failed to pass a budget for a new fiscal year or a continuing resolution as a stopgap for a few months. What followed has been really a partial shutdown of the government. Money for things like operating the national parks has run out, but 鈥渆ssential鈥� services like national defense and air-traffic control are still funded.
The debt limit, by contrast, comes due periodically so long as the government is spending more money than it takes in (which, admittedly, is most of the time). Congress sets a limit for how much money the Treasury can borrow to pay US bills, and when that is no longer enough, Congress must raise the debt limit or end deficit spending. President Obama has described a vote to raise the cap as a vote 鈥渢o pay the bills on what Congress has already spent.鈥�
