That said, there is a reasonable concern that Congress just won't get around to fixing it and so there will be an automatic cut. But there is no law that I'm aware of that says SS must be self-supporting and can't receive money from the general fund.

SS is not self-supporting. It has not been for decades.
The money that is collected from SS payroll deductions goes into the general fund and the money that gets paid to recipients come from the general fund.

They just play bookkeeping games to make it seem otherwise. It's just like you putting your paycheck into your lefthand pocket and then lending it to your righthand pocket as a loan that pays interest. Like lending money to your wife. Just smoke and mirrors. It's all the same pot.

Congress will rescue SS by increasing what is collected from paychecks. Recall that up until 1994 there was a cap on the Medicare deduction, which they removed the cap so they could collect more money when Medicare "ran" out of money. They'll do the same to SS deductions, and probably increase the percentage.

The problem with continually kicking the can down the road is that eventually you run out of road.