It's worth mentioning this happened under a Democratic president and Republican congress, not far from what we have now.
[0]https://fred.stlouisfed.org/series/FYFSD
Edit: added citation
How much would spending need to be cut by, what programs will actually accept these cuts, how much can taxes realistically be raised by, why won't there be lobbying/special interest/loopholes to prevent this?
You could also try to raise taxes without stifling growth (and thus reducing revenues), but that's an even harder technical problem to pair with a similar political problem. Personally I'd be in support of a constitutional amendment that caps Federal revenues at 20% of GDP, so I wouldn't be on board for this, but to each his own.
Take a look at page 39 in the latest budget summary[0] and see if you can find the right places to raise revenues and cut spending to eliminate the $1.148 trillion deficit for 2023.
[0]https://www.govinfo.gov/content/pkg/BUDGET-2022-BUD/pdf/BUDG...
In 2023, half the members of Congress believe in Qanon and Jewish space lasers. And the same is true of the voters.