I have a leaf blower and I think I ran it with too little oil and now the cord will not pull through to start the machine. Is there anything I can do to fix that?

Probably not, running w/o proper oil/gas ratio will cause the engine to zeize/lock/crack and it will be too costly to repair.

Rbm maybe correct, but you could try this,
Remove the spark plug and spray the best penetrating oil you can find into the spark plug hole, I prefer PB Blaster, and allow it to set for an hour or so. Then try to work the cord, if no results, remove the covers to the engine to gain access to the fan or the flywheel, and try and work it back and forth. If this works, keep working it until it moves freely. And if it works, the engine will never be quite the same again, but it will possibly get you by. If this does not work, scrap it.