My current employer asked if I'd like them to reconsider my current salary
It means your current employer values you significantly – it takes significant time to train new employees and allow them to settle in the team/workplace. Assuming you didn't burn any bridges when you turned them down earlier, the smart thing to do here would be to save your own financial situation and look out for yourself. That's what any reasonable company would do as well.
Note that many major financial institutions have declared that we are either undergoing a recession, or are at the beginning of it. I assume that you want to take an incremented salary if you were to continue at the same place. Staying at the current salary would convey a message of desperation making you lose the leverage, so I wouldn't go straight ahead telling them how bad it is, around the delay in joining date, though them guessing it on their own is a possibility.
Since the timeline involved are only of week, go back to your current employer, and let them know that you gave a deeper thought to their offer of improved compensation. Let them know that you would be open to considering their offer if they can meet your expectations. If asked on what made you change your mind – be prepared to respond with a reason which sounds true – could be around commute, family considerations, or minimising future risks of layoffs due to upcoming downturn.
Remember, one must not bring their ego into such discussions – be wary of your own emotions around feeling embarrassment to ask for a reconsideration. In any case, do not share with the current employer the information that you've been asked to hold joining the next company – this will negate any kind of potential salary increment you might get.
Be ready with range of ballpark numbers for them to consider – your existing offer letter can serve as a strong data point if it's not much out of their reach. Based on the terms offered, decide if you want to continue or stay at home waiting for a job that may never begin. Depending on your personal commitments, be prepared to work at the existing salary that you had before resigning.