come within an inch of (something)
To almost get, achieve, or experience something. She came within an inch of the gold medal, but her leg cramped in the last few meters. Hundreds of people came within an inch of death when their apartment building caught on fire in the middle of the night.
come within an inch of doing something
Fig. almost to do something; to come very close to doing something. I came within an inch of going into the army. I came within an inch of falling off the roof.