He's also admonished fellow Republicans that they may find themselves negotiating with Democratic leader Sen. Chuck Schumer of New York if they don't close ranks. In that case, McConnell said he'd aim for a limited package propping up troubled insurance markets around the country.
The Gallup-Sharecare survey serves as a kind of early indicator, publishing several months before the nimblest government surveys. The most recent government report found that progress reducing the number of uninsured stalled in 2016, after five consecutive years of coverage gains under Obama.
Peering at this year, Gallup-Sharecare found an erosion of progress, with the number of uninsured edging up again. It estimated nearly 2 million dropped out of coverage.
The losses were concentrated among younger adults and people buying their own health insurance policies, the survey found.
That may be a reflection of rising premiums and dwindling choices in the insurance markets created under Obama.
Also, President Donald Trump has branded his predecessor's leading domestic achievement a "disaster" while pursuing its repeal. Insurers say Trump administration actions are contributing to double-digit premium increases for next year.
Gallup-Sharecare found that the uninsured rate rose by 1.9 percentage points among adults aged 18-25 since the end of last year, and 1.5 points among those aged 26-34.
Participation by young adults is considered vital for keeping health insurance premiums in check. But young adults are also likely to enjoy good health and may not recognize value in having coverage.
The Gallup-Sharecare survey is an ongoing effort based on interviews with about 500 people a day. It was previously called the Gallup-Healthways Well-Being Index.
Results are based on telephone interviews conducted April 1-June 30, with a random sample of 45,087 adults, aged 18 and older, living in all 50 U.S. states and Washington, D.C. The margin of error is plus or minus 1 percentage point.