When data doesn't compare like you think it should, the first tool in your toolkit is the print statement. Just add print user_input and you'll find its an instance of the usr class, not the user input. You stored that in an instance variable called inp. As an aside, in pythnon 2, you should inherit from object to get a new-style class. You don't need to do that in python 3.
class usr(object):
  def __init__(self, inp):
    self.inp = inp
    if inp == "abc":
      print 0
      exit()
user_input = usr(raw_input())
if user_input.inp == "123":
  print("1")
else:
  print("No")
If all you want to do is validate the input and not store it, a function is a better option. It can just return the validated string. It can do other prettying up of the data also. In this example, I also strip whitespace from front and back so minor input errors are ignored
def usr(inp):
    inp = inp.strip()
    if inp == "abc":
      print 0
      exit()
    return inp
user_input = usr(raw_input())
if user_input == "123":
  print("1")
else:
  print("No")