I'm not sure that it's a fair characterization that Obama care saves money. If it did, why did the medicare tax have to be extended to investment income, or why do high-value medical plans have to pay a luxury-tax, and why do we now have to pay a sur-tax/sales-tax on medical devices (which were previously exempt from transfer/sales tax)? It's because this money was required to pay for premium subsidies for "poor" people and for medicare expansion parts of the ACA.
We may be getting more value for the money we spend (more people covered, less overhead), but we are certainly not saving money.
Because of the fact of the federal subsidies (not the actual cost of services), in fact the more "poor" people sign up, the money that funded these subsidies came from taxes the "rich" must pay under the new law. Given the definition of rich these days (i.e., $250K single, $400K married), I imagine many if not most doctors fit that description...
Unfortunately, the real folks that get screwed under the ACA is the middle class. They make too much money to qualify for subsidies, they probably had reasonably good insurance already (equiv to gold/platinum which have fairly high premiums which are subsidized by the employer and the lowest out-of-pocket and high coverage percentages), but now they have to pay marginally more taxes and their premiums went up drastically to cover the expected increase in enrollees in these types of plans with pre-existing conditions (who don't mind the higher premium because they really need the benefit of high coverage percentage plans to reduce their out-of-pocket expenses to the 10% level of the platinum plan rather than the 40% level of the bronze plan).
As a result, many middle class are probably better off financially by avoiding the gold/platinum plans and switching to a high-deductible plan and putting their premiums into a health savings account, but that greatly increases the amount of paperwork they have to do (not a problem if you are rich and have an accountant to take care of this trivial stuff for you), so many middle class are likely to just end up subsidizing the folks with pre-existing conditions (I assume that even if you disagree doctors are rich, they are at least middle class, right?).
It appeared that there was some hope was that younger single people would join the ranks of those getting screwed because they would be "forced" to pay for insurance that they wouldn't use. However, it appears that those that didn't qualify for subsidies seem likely to not get insurance and not pay the fine (they don't appear to be signing up). Apparently the penalty for not paying the fine appears to be low and the IRS admitted they have no way to know if they need to fine someone (because they don't have a way to verify anyone has health insurance) short of a taxpayer audit so the offender must essentially voluntarily pay the fine.