That statement is one of those things that is both true and not at the same time. Oh sure, perhaps 20 million more people have insurance and no doubt at least some of them have greater access to the healthcare system than they did before. But there are some other considerations.
There are three terms related to healthcare that are sometimes used interchangeably and do have some overlap but are distinctly different things: insurance, coverage, and access. "Insurance" is a policy to pay for some portion of someone's healthcare costs for which someone pays premiums on behalf of the individual. "Coverage" is a separate mechanism that will pay for some portion of someone's healthcare costs; things like Medical for the poor are the prime examples. "Access" is the ability to actual get a healthcare provider to provide healthcare to you.
To see the distinction, let's say that everybody in the world had healthcare insurance but either there were no healthcare providers or none of the healthcare providers accepted the insurance as payment. Then everybody has insurance but nobody has access.
"I worry about giving 30 million people a card and a false promise." Dr. Atul Grover, Chief Public Policy Officer American Association of Medical CollegesSince there are almost exactly an identical number of healthcare providers per capita now as there were before Obamacare was enacted, and healthcare providers have always been pretty much fully booked, and the healthcare system at the provider level is not noticeably more efficient (and is perhaps less efficient), for each bit of healthcare that is provided to someone because of Obamacare, a corresponding bit is not, almost by definition, provided to someone else. In other words, with an equal number of booked providers per capita, total services, procedures, etc. remain constant. This one really is close to a zero sum game and is severely stressing the system:
The health care workforce is already facing a critical shortfall of health professionals over the next decade. The ACA breaks the promises of access and quality of care for all Americans by escalating the shortage and increasing the burden and stress on the already fragile system. The ACA’s attempts to address the shortage are unproven and limited in scope, and the significant financial investment will not produce results for years due to the training pipeline. With the ACA’s estimated 190 million hours of paperwork annually imposed on businesses and the health care industry, combined with shortages of workers, patients will be facing increasing wait times, limited access to providers, shortened time with caregivers, and decreased satisfaction. The health care workforce is facing increased stress and instability...Obamacare is about playing god, literally deciding who lives and dies, since for each person access is provided, it's taken away from someone else.