I think the opposition wanted to toss the entire ACA system calling it a tax. However, SCOTUS took a more piecemeal approach than the opposition wished and removed the bit they felt was a tax and left the ACA unaffected generally.
The 2017 TCJA removed the individual mandate. Presumably, that is what FrustratedMonky and kccqzy are referring to.
Obviously, the ACA made it so all health insurance premiums have a large "tax" component, due to the extremely narrow underwriting criteria health insurers are allowed to use. The individual mandate had previously applied a tax to all taxpayers, but after TCJA 2017, the tax is only paid by people with health insurance.
>Enacted in December 2017, the Tax Cuts and Jobs Act (TCJA) reduced the shared responsibility payment to zero for tax year 2019 and all subsequent years.
I don't think the opposition was using 'its a tax' as argument to cancel ACA, since the SC Ruling that saved ACA was made by saying congress is allowed to created taxes, and this was a 'type of tax'.
If calling it a tax saved it, that would then not be a good argument to get rid of it.
SCOTUS has been reasoning backward from their blatant partisanship for a couple decades now. It used to have a bit of randomness with some justices defecting with "reasoned arguments", but that's basically over now.