Why does a broker go about closing the stock position if in case of the spread his risk didn't change after the assignment? The risk remains the same after the assignment as it was at the time the spread was opened: the stock position is hedged by the long option. This makes little sense especially because for the options the risk is easy to calculate.
Someone has to pay for the stock. If you don't have enough funds (or buying power) in your account to pay for the stock, you have to do something (and if you do nothing, your broker will do it for you) to cover the cost of the stock put to you. Joe.
The broker pays for the stock and the trader pays the interest on the borrowed money at least temporarily. There is no need for the broker to liquidate the position in a urgent manner because those are not the naked options and not all the money borrowed from him is at risk. Isn't that what portfolio margin is for - to let borrow money based on portfolio risk? If software calculates risk correctly the buying power should not change by much after the assignment.
Margin rules are different for stock and options. If you don't have the funds to purchase the stock (Reg T margin for stock is 50%), it's a margin violation and therefore you must either put up the extra cash, close the stock position directly or exercise an option that buys (sells) the stock, creating an offsetting stock position.
As mentioned above, don't worry about assignment, unless you foolishly allowed the calendar to go deep underwater. Somewhat off the topic, but I think you will find that you get better risk/reward by keeping only one or two months between the front and back month. I personally think roll-over is not a good idea. The trade should stand on its own. Also consider calendars with 45-60 days before expiry. Just a suggestion.