Why take the chance? I don’t know what B of A’s turn times are right now, but they do have a reputation for not being able to perform. When they took over Countrywide there were tons of horror stories (I think you can find some on this site) about the loan process taking months, locks expiring, lack of communication, etc. etc.
One of the main reasons for using a broker vs. a bank like B of A or Chase is that the broker can submit your loan package to be underwritten by a couple of different lenders, something I do routinely on purchases. After 20 years in the business I am still amazed at how differently two underwriters can view the same loan. If you get a sticky underwriter (or declined) at B of A, you will have to start all over somewhere else and may not close on time. On the other hand, if your broker has submitted to two lenders and one doesn’t like your loan, you just go with the one who does and you haven’t missed a beat.
As far as pricing goes don’t forget that loan rates change every day, sometimes more than once during the day. If you want to compare apples to apples you need to call B of A, SDCCU, and your courteous, experienced, good looking mortgage broker and ask them to send you a rate quote, good faith estimate and fees worksheet (this is important – the new gfe doesn’t list all the fees as well as the old one did, so ask for the fees worksheet which breaks down all fees) on a 30 day close, at noon the next day (the same time and day for all quotes).
After you’ve picked your lender get ALL your documentation to them and get pre approved before you find a home and open escrow, and a 30 day close should be no problem.
Sorry if this post is self promoting, but I do believe a good broker can usually do a better job for their clients!