Personally, no.
If the job was really that good then I'd consider it short-term whilst I looked to relocate but certainly wouldn't consider it a permanent option.
Even short-term, I'd be looking to stay over at B&B at least 4 nights/week.

If the job was the nuts then I would consider living there during the weeks. 350 miles commute? No.

I would consider 350 a foreign trip rather than a commute!

I did a 120 round trip commute for 6 months.
There was 5 of us car sharing so only drove once a week but I was completely sick of it and was happy when the 6 month contract was over.

There's a lot that can happen over that sort of distance and all the little hold ups and niggles in traffic etc build up and drive you nuts.

I'd say it's too far.

I commute by train and do 2 hours door to door, in each direction.

350 miles! You'd have to be mental to even consider it. You'll spend all your time commuting or working and then spending weekends completely knackered and recovering. Your personal life will suffer, as will any relationship not to mention your health.

If the job is that good then move or rent digs. Could you arrange to do compressed hours so you work away and do your hours in 4 days instead of 5? That way you'll spend more time with your family/friends at weekends to make up for being away during the week.

As has been said, I'd only entertain that on a 4 day week, staying Monday, Tuesday and Wednesday nights. And it'd have to pay well to make it worth while.

Agree with all that has been said so far. I was considering a job up in Brackley and commuting from the East End of London. The job was amazing and I was really up for it. Sadly I never did hear back and in hindsight even that (circa 220miles round-trip) was too far.

350miles a day is just insane. Your car would have intergalactic mileage on it in no time. What about when the weather gets bad in winter?

If the job is worth it and the pay is good enough maybe consider renting a bedsit or lodging with someone?

As for the time element, I've come to the conclusion that when working a "job" (i.e. working for a company/someone else) anything much over 1hr30mins door-to-door is too much. I was offered a job in Fulham with a very good salary but turned it down for a number of reasons, one of which was the time involved in the commute. It's not far but by Tube it's a good 1hr30-2hrs and I just didn't fancy it. 3-4hrs a day travelling is tough going and it does take it out of you.

forget it

Personally it's not a case of 'how far' but 'how long'.

My own personal limit would be 1.5 hours each way. I used to drive 60 miles each way to work and this would take me c.1 hour as it was on a dual carriageway and against the main flow.

I'd be interested from the OP how this job came about. If he applied for it, surely he must have known the location and must therefore have been 'happy' with it. If, however, he was head hunted then would the company come to some arrangement to put you up somewhere for a period, even if the OP paid some of the accommodation costs?

If it's an amazing job then I'd rent there through the week and look at moving there permanently if it works out. A 125 mile commute is crazy talk.