My wife and I want to have new tile put in our kitchen, two bathrooms, laundry room and front entrance.  All off this comes out to a little over 300 square feet and *we already have the tile*.  

We had a contractor give us an estimate to pull up the linoleum and put in the new tile.  His estimate was almost $4500, which is about $15 per square foot.  Does that sound reasonable?  We're planning on getting more than one estimate, but there are a lot of knowledgeable people here so I thought I'd ask...

What is under the linoleum? Is it tile ready concrete or wood? $4500 sounds high but more info is needed on the scope of the work.

There shouldn't be anything under the linoleum except concrete and, presumably, some sort of adhesive for the linoleum.

Is he tearing up the linoleum and cleaning up the god awful mess under it?
ETA: good point below, IIRC with stone tile you have to butter both the wall and the tile (not sure about floor tile), which drives the cost up.

Yes.  

EDIT:  They would be pulling up the linoleum and doing whatever they have to do to the concrete under it for all 300 or so square feet.

If the lino is stuck, and there is non hydrostatic pressure ( water pushing up from below the concrete ) the its best for the lino to stay.  Its a great slip sheet membrane and could keep your tile from cracking if the slab gets a crack in it.

In my part of the country, that price is way high.  Having said that, I can't see what then job looks like from here.  Are you doing ceramic or natural stone?  Make a big difference in the price.  I've been in the tile trade over 30 years and have done acres of floors.

It's ceramic tile.  Is one more difficult to work with than the other?

And we're both in CA, so your part of the country is the same as mine.  

And how can we/they determine if there is stuck linoleum and/or non-hydrostatic pressure?

I would want Ditra under the tile.  Adds cost but you'll never have a cracked tile.  You might without the Ditra even on concrete.  

The price sounds ok to me.  Not a cheap price but then you don't want crappy work when having tile work done!!!!  It's on the high side but not totally unreasonable IMO.  You have several rooms to do so there will be a decent amount of intricate cuts.  Would be cheaper if you were just tiling one large area.

You are aware that this is the Do It Yourself forum right?  Why not just do it yourself?