Generally, looking at the last 30 years or so, it is evident that voters do not care about this issue very much.
RE the budget surplus, the dotcom boom led to a large increase in taxes collected which collapsed from 2000 to 2003. Similarly countries naturally spend more when their population is either skewing old or skewing young. The US hit peak working-age demographics during the period you are describing. The outcome doesn't seem to be "engineered" so much as accidental. In fact taxes on balance were cut during this timeframe while significant contributors to the long term debt / future crisis were unleashed (glass steagall repeal which arguably led to the great financial crisis & federal loans for eduction were dramatically expanded without oversight to ensure the money was being well spent).
Similarly, the covid response caused an explosion in the budget deficit which I wouldn't blame squarely on "a candidate's economic policy". The 2023 deficit in real dollars and as a % of GDP the largest (by a fair amount!) outside of a war, economic crisis, or the covid response. This doesn't even count the ~400? billion in student loan forgiveness that was attempted and failed.
"Generally, looking at the last 30 years or so, it is evident that voters do not care about this issue very much" <- 100% agree.
How that relates to the (relevant!) factors you raise is that firstly, most of them were knowable at the time. Bush knew that tax revenue was falling when he proposed his tax cuts. He also planned two foreign wars without planning to pay for them. These were choices that were quite obviously, without the benefit of hindsight, going to lead to increased deficits.
Covid was unpredictable, but the administration had choices on how to handle the deficit spending. Notably, they did not choose to increase revenue in any meaningful way. And the administration was not blocked by Congress in this, raising revenue was simply not a concern mooted by the Executive. (They did not even add spring-loaded revenue increase that would trigger when the economy recovered.)
These choices to increase the deficit were made will roughly all the information we have now. Both choices were contemporaneously derided by deficit hawks; it is not a surprise that they raised the deficit.
But again, Dick Cheney was correct that deficits do not matter (to voters).
I'm not linking to sources because people feel the need to find the sources or they don't believe them. But there are a number of graphs of the numbers available on the Internet.
Suffice it to say that any adviser advising a presidential candidate to pay any attention to the deficit beyond lip service is doing that candidate a disservice, as voters have shown time and again that they simply do not care.
The last president to attain a budget surplus was indeed a surprise for me.
[1]: https://www.investopedia.com/us-debt-by-president-dollar-and...
But Presidents typically take credit for their legislative wins, so we also give them credit for budgets they sign.
(It is also the case that one measure of the efficacy of an administration is the quality of the budgets they are able to coax out of Congress.)
Largely speaking democrat administrations reduce the deficit while republican administrations increase the deficit, despite this being the polar opposite of political talking points.
I remember the budget hawks in the aughts saying that if the administration wanted to spend a ton of money on wars in Afghanistan and Iraq (this: unrelated to 9/11), that it would be fiscally prudent to raise tax revenue to cover the costs. Bush instead cut tax revenue substantially.
I'm not making a judgement either way, just saying that there was a choice here and Bush made the choice to increase the deficit. (Dick Cheney was correct when he advised Bush that deficits don't matter. The increase in the deficit indeed didn't matter to the electorate, and the deficit spending, in part via tax cuts, did win him a second term.)
How old are you? If you're a Gen-Xer you should remember Clinton's surpluses if you followed the news:
* https://www.brookings.edu/articles/a-surplus-if-we-can-keep-...
Then Bush got in (beating Gore by ~600 votes in Florida to take the Electoral College), and then did tax cuts and later war spending:
* https://en.wikipedia.org/wiki/Bush_tax_cuts
* https://www.cbpp.org/research/the-legacy-of-the-2001-and-200...
More recently, when the GOP controlled Congress and White House (Trump), they did a bunch of tax cuts:
If you want to argue that presidents are not responsible for laws bearing their signatures, I stridently disagree.
As Presidents typically take credit for their legislative wins, we also give them credit for budgets they sign. (And then we name them things like "Reaganomics.")
Amusingly, the two Reagan tax cuts are notable exceptions, passing the house with overwhelming majorities despite Democrat control.
The budgeting process is a huge hairball of political Rube Goldberg contraptions, and who "proposes" the budget on paper has very little to do with the actual political maneuvering involved. As far as the point of this discussion is concerned, both Congress and the President are responsible, since both branches are deeply involved in the political maneuvering.
In that election the democrats had net gains in both houses of congress, the democratic presidential candidate won the popular vote, and the presidential election was won by 537 votes. I don't know how this could be called "soundly rejected."
> financial problems in the United States transcend political party
Correct, in part because voters do not care.