What is the average cost/timeframe of obtaining a pilot job at a major passenger airline in the US?
The distribution of how pilots get to the majors is bimodal. 

If you can get a military pilot slot and give 4-10 years to the USAF, you can then get an FAA ATP and start interviewing at whatever majors are hiring and have your ex-mil buddies on the hiring board. Great way to get in at FedEx or UPS. This costs a few grand for your ATP but that's about it. 

If you can't get a military slot, getting up to the point you can instruct from nothing can vary wildly in cost. The accelerated flight training programs will do this for around $70,000. Next you instruct until you hit 135 mins and do either that or instructing. At this point you shouldn't be paying for time anymore. When you get on at a regional you'll sit right seat for a few to many years then you'll upgrade. After about 1.5-2 years in the left seat you'll have the bare minimums to apply at a major.