Regardless, the 2023 budget is the law. Congress has already authorized that money to be spent. The executive branch must, by law, spend that money. They have no discretion in the matter thanks to the laws passed after Nixon kept impounding funds that he didn't want to spend.
The debt ceiling was actually created during WW1 to make it easier for the government to spend money without having to constantly bother Congress about it. That it's being used to force a default now is ridiculous. And let's not pretend that this is a both-sides thing, either. Only one side constantly does this. But, I suppose that we can't get too political.
In any case, we've been told by multiple high-ranking officials that there isn't really a way to prioritize one kind of payment over others. The system isn't set up that way and there's no law to allow it, anyway. So, if we do default, then Social Security, government salaries, and every other kind of payment are equally likely to be reduced or delayed until the debt ceiling is lifted or we find some other way around it. Hopefully, it doesn't come to that.