Python 3 2, 79 74 69 65 68 bytes

def f(n):i=l=len(`n`);s='';exec n//l*"s+=`i`.zfill(l);i+=l;";print s

byte count increase from bad output method

Python 3 2, 79 74 69 65 68 67 bytes

Thanks Dennis!

def f(n):i=l=len(`n`);s='';exec n/l*"s+=`i`.zfill(l);i+=l;";print s

byte count increase from bad output method

Python 3 2, 79 74 69 65 bytes

TO BE EDITED

def s(x):
 i=l=len(`x`)
  while(i<=x):print"\b"+`i`.zfill(l);i+=l

My new model is based on Karl's model based on my model, I'm not sure if that is fair or not apparently, the printing police have visited and said I can't use backspaces ;_;. Edit forthcoming

increments the number to be printed by length of input, prints it with proper amount of zeros, until number is equal or greater (shouldn't be greater though)

\b is backspace

Python 3 2, 79 74 69 65 68 bytes

def f(n):i=l=len(`n`);s='';exec n//l*"s+=`i`.zfill(l);i+=l;";print s

byte count increase from bad output method

Python 3 2, 79 74 69 65 bytes

def s(x):
 i=l=len(`x`)
 while(i<=x):print"\b"+`i`.zfill(l);i+=l

My new model is based on Karl's model based on my model, I'm not sure if that is fair or not

increments the number to be printed by length of input, prints it with proper amount of zeros, until number is equal or greater (shouldn't be greater though)

\b is backspace

Python 3 2, 79 74 69 65 bytes

TO BE EDITED

def s(x):
 i=l=len(`x`)
 while(i<=x):print"\b"+`i`.zfill(l);i+=l

My new model is based on Karl's model based on my model, I'm not sure if that is fair or not apparently, the printing police have visited and said I can't use backspaces ;_;. Edit forthcoming

increments the number to be printed by length of input, prints it with proper amount of zeros, until number is equal or greater (shouldn't be greater though)

\b is backspace