I don't think a contractor would cost you that much less. And you would have zero legal recourse if his opinion was wrong, as he isn't technically qualified to give an opinion on the subject. You also may need the engineer's report for the permits application from your municipality. You need to check with them about any design drawings and inspections that they require for the project.

Thanks for the input. My house is a ranch, so there's nothing to support above it, but the roof. We're taking out a load bearing wall that separates the living room from dining room, and the contractor will replace this with a flush beam. One end of the beam will be supported by an outside wall and the other end will terminate on a small wall that sits over a post in the basement. I get the feeling that my contractor has done this a lot and feels pretty comfortable with that arrangement. Meanwhile, I've noticed that my living room runs the full width of the house (24') with no support other than a homemade truss arrangement for the roof, that I understand was common in the early 1960's. This arrangement has stood the test of time, so I guess it's okay, but I still get a bit nervous when there's a large amount of snow on the roof. I had asked the contractor about installing a beam over the living room as well, but he was a bit more hesitant about that, and merely said he would look at it when he starts the kitchen work. So I guess the answer is that an engineer would be needed to decide if/how additional support could be provided in the living room. That's probably why my contractor is hesitant to give me a firm answer.

I strongly disagree. I studied structural design for longer than most engineers and have been practicing architecture for 50 years but I would never modify a lateral bracing system for roof trusses without the help of a structural engineer even if I had the original structural drawings and calculations. In too many cases I have learned from an engineer that the original design was inadequate to the point of being dangerous. I just finished a project where the owner did not want to pay for an engineer but when I told him I would have to resign he agreed to hire one and was shocked when he learned that the structure of the building had never met the building code or acceptable engineering practice. I had to explain to him that a structure was not "grandfathered" since it did not meet the building code when it was built. His contractor was very capable and thought he could modify the structure himself. the structural reinforcement he had already done had to be replaced. He thanked me later for intervening. Advising people to rely on contractors with little or no structural training could cause them serious harm.

You need to have someone that knows about load bearing walls (not just someone off the street), to come in and do a thorough inspection. They will need attic access, to do this. As to those two 2x4 you want to remove, well, you can be assured, they were not just put there, because someone wanted to put in some 2x4. They are there for a very good reason. Its just the way the house was built., so dont remove anything more until you get it inspected.