No increase in the debt limit is this:
The Government's current level of spending is approved, but an increase in spending [[AKA more borrowing) is not authorized.
Which means - The Government must make budget cuts for the Government to pay it's bills in order to not exceed it's current level of spending. In actuality it means the Government stops borrowing money it can't afford to pay back.

It may be tough on our free spending Government, but it would in effect show the Government is being financially responsible for the first time in 40 years.