Brandon,
When it comes to investing in single family homes, I'm sure you are aware that the rules change slightly when dealing with homes held in an LLC. Initially, a bank is going to qualify you on your first 4 homes based on 20% down and the reserves they require will be limited to that property. When you are dealing with home 5-10 you will most likely require 25% down and 6 months of reserves for all of your properties in liquid capital, although there might be some ways around the liquidity requirement using potential investment income although most lenders require 2 years of seasoning before they are willing to do this. Making a loan specifically to an LLC is not directly possible due to the rules that Fannie Mae and Freddy Mac have set forth. They will not allow for entity investing, requiring that the loan be in your personal name or the name of a irrevocable trust. Given that they may lend to a trust, there might be some creative ways to structure the deal but you would have to speak to an attorney who specializes in entity structure for that.
In response to your question about calling a loan, just about every lender out there will have a due on sale stipulation in the contract requiring that the note be paid in full when there is a title transfer. Whether they follow through with this is going to be up to them, and will depend on a variety of factors. I have never personally heard of a lender doing this, but if you were to attempt it you just have to realize that there is risk involved.