One of the things lost on so many pro-universalists (for lack of a better term) was that the solution to "not everybody having health care" was "find a way* ".
And "find a way" was synonymous with "government-run, single-payer health care".
The first time this came up under Clinton in 1993, the medical insurance industry said, "f-it. We'll just cover everybody." That is, of course, a suggested solution. But it's not the one in accordance with getting people dependent on government care for the purpose of getting re-elected, something the Clintons publically stated they wanted to do, just like, they said, FDR did with social security, which FDR also publicly stated, and which is often posted on the wall of the round room that displays the Constitution and the Declaration of Independence in the National Archives building.
* With the attendant implication "...that doesn't leave people worse off".