We put in our offer with a "acceleration clause", saying we'll pay a certain amount over the highest bid not to exceed $--------. 

The lender has the right to accelerate the mortgage, calling it due and if not paid as demanded may the foreclose.

Some might accelerate their purchases of real estate in overseas countries now

(aka accelerated depreciation.

If you don't pay when they accelerate the note, what happens?

You may have an accelerated amortization on one part and a longer amortization on another part.

In such a case, any amount remaining once all debts and costs have been satisfied shall be returned to the mortgagor.Conversely, when the mortgagor has little to no equity in the property - particularly where the equity is less than the sum of all amounts owed, the court may shorten the redemption period and, at least in our experience on this end of the Country, enable the lender to take possession and sell the property at a price between what is owed and FMV.2a) When you reach the stage where the lender has filed a Statement of Claim, the note extended to the mortgagor has been accelerated and is due in full (principal, all accrued interest and any costs or penalties).   2b) During the redemption period the mortgagor has the right to redeem (buy back) the property.  

We can take straight depreciation, or accelerated depreciation on certain components in the complex too.  

But, I feel the need to accelerate this now.

This would consist of 3-5 people (ideally in the bay area) that are very serious about accelerating their real estate investment goals and learning.