Certainly, I'd agree with you that the Republican congress was responsible for balancing the budget, It's one of the reasons why I voted for John Kasich in 2016 primaries, he was the house budget committee chairman. Of course, it was much easier to balance the books when the economy was booming in the 1990s.
Regarding Obama, the deficit did in fact go down, he didn't impose major cuts, but he did raise taxes. And the economy was growing hence budget revenue increased. The graph shows the budget deficit since 1981.
Regarding the deficit, I think an interesting point to make is a comparison with Europe. Here are, for example the criteria to join the Euro (not like the US would ever do that, but it is an interesting thing to look at to get an idea of "how" the deficit should be ran)
As of now, the EU mandates a maximum deficit of 3% under normal circumstances (ie without covid-19).
It also mandates that the debt/GDP ratio of the country must be either:
a) Below 60%
b) Declining by at least 5% per year on a 3 year rolling average
So if in terms of the deficit, the US are failing miserably, with a 4.6% budget deficit and a debt/GDP ratio of 107% with no real declines
If the United States were an EU country, they would not be in the "good economies" club along the likes of Germany and the Netherlands; but rather on the "finanacial disasters" club alongside Spain and Greece.
It does not matter at all since the US has a lot of other advantages compared to Spain/Greece (literally "haha money printer go brrr") but it is still a bad sign
