Debt limit
The debt limit (or debt ceiling as it is sometimes called) is a self-imposed cap on the amount of borrowing the United States government can make from other entities (the people, foreign governments, etc). Since the limit is self-imposed, it can also be arbitrarily raised or lowered on the vote of Congress.
Reagan Speech Relevance
In 'A Time For Choosing', Reagan explains that
We have raised our debt limit three times in the last twelve months.
These increases are as follows:
Aug. 31 1963: raise to $309,000,000,000
Nov. 26, 1963: raise to $315,000,000,000
June 29, 1964: raise to $324,000,000,000
Source Links
Limits on Federal Debt: 1940–Current (whitehouse.gov)