US pharmaceutical companies aren't happy that the NHS uses its bargaining power to pay a very low price for drugs and want any trade deal to raise the price paid. Given that that is a substantial proportion of the NHS's spending, that would have knock-on consequences.
That has literally never happened and I think a large part of why Labour is failing is that they are unable to grasp the NHS argument no longer works. Labour has insinuated roughly 600 times that this or that Tory bill would be the end of the NHS and would lead to it being sold off.
It's a boy who cried wolf argument that's not going to work or change anybody's mind anymore.
It keeps being used because it remains one of Labour’s most effective tools. The rhetoric becoming staler is offset by the population growing older and more dependent on it.
They are further underwater on other major issues than they are on the NHS.