A lot of people know that business organizations and the American Medical Association opposed Truman's national health care push. They don't realize that organized labor did as well .
But it did. As discussed in the great new book "The Age of Acquiescence," per my review, the New Deal "settlement" between labor and management-ownership in America was that organized labor would accept the financial settlement of wage gains and benefits offerings (which became more important during World War II with wages generally frozen or nearly so), in exchange for eschewing German-type unionism of sitting on corporate boards (see Volkswagen of America today) and other broader attempts to alter the labor-management power relationship.
So, in Truman's time, the bennies, including good private health insurance, that came with a union job, as well as the pay itself, were a recruiting incentive, and one that organized labor wasn't going to surrender, not even if this helped change the labor-management power relationship to the working man's benefit in general.
Even with LBJ's moves, and without formally stated opposition by organized labor, surely this is why he settled for Medicare and Medicaid. Senior citizens normally are retired and therefore not candidates for union job recruitment. Poor people are working in low-paying non-union jobs, if working at all; also, therefore, not part of organized labor's orbit.
That said, Truman was proposing something more than just national health care. He wanted a federal hospital oversight agency, and a federal form of workmen's compensation for work time lost due to medical treatment. That said, the Truman Library claims that organized labor was in support, but this is the first time I've seen such a claim. I've generally read elsewhere that, if not opposed, it was no more than neutral.
Anyway, the combination of ideas in the bill might have been better than just single-payer health care.
First, Truman probably could have said that, if surgery were needed, it would only be compensated for if performed at an accredited hospital. That, in turn, would have opened the door to federal pricing controls, including saying "no" with a capital "N" to outrageous pricing by Big Pharma.
(Today, the JCAHO only partially performs the accreditation idea, and as a private agency, doesn't have the same teeth that a federal regulatory board would.)