The deficit is based on the budget, they're basically 1:1. It's the difference between what we spend versus what we collect in a fiscal year. That speaks to an administration's ability/willingness/desire to make the revenues and expenses closer via the legislative (or other) processes. All debt isn't bad debt and people often engage in fallacies of composition when they think about national debt versus their individual households. The level is the debate - which is part of the reason we end up with the debt ceiling debates.
For sure there are obligations that continue over time and span administrations, no debating that, but I'm not sure what you're getting at with lagging indicators that you've mentioned. For sure there are bills designed to make the next person look bad, no doubt about that.
I'd argue that it's not partisan to point out factual information about which administrations have done better with that balance. But either way, I'm certainly not arguing that Democrats are perfect. I happen to think they're an absolutely horrendous operation.
First, I agree that the current operation of our congress is an obstructionist sh*tshow. I'm sure we all have various ideas about how we got here. It wasn't always this way. We've lost a lot of statesmen in the past 15-20 years and have replaced them with caricatures. Blame the rise of social media, disinformation, or whatever you prefer. We're made to believe that anyone who doesn't share your opinion is your enemy. It's sad, really.
The answer to how to fix this or anything else someone considers an issue, like most things that are political, is that it depends on what your priorities are.
If we think that our debt load it too high, we have to either spend less, increase revenue or a combination of the two. But the devil is always in the details and, even at that, you're relying on politicians to do the "right" things.
The way I see it, those priorities change amongst politicians (and voters) depending on who is in the White House and the balance of congress - and that's why nothing ever seems to get fixed.