Would it be federal, or state-wide? How would it be funded? Would it be public "option", or would private pay be banned like in Canada? How would compensation rates be updated, and how often? Ask any hospital administrator what they think of Medicare/Medicaid rates, and they'll probably answer that they're set too low and that they lose money on Medicare/Medicaid patients.
The details on "universal healthcare" can range from heavily-regulated private insurance - Germany for example - to outright bans on private pay for items insured by the government (Canada). A lot of Americans seem to want some sort of federal system that provides insurance for everything, which seems like the best way to get the most expensive, least capable system imaginable. Imagine having yet another insanely expensive, totally underfunded entitlement program that politicians can continuously pad with new promises every 2-4 years when they need to get re-elected.
The Canadian experience (source: Canadian currently living in the US) is one you do not want to replicate, so be wary - Canadians have little confidence in their system at this point, even though it's quite expensive relative to European peers - and we have shockingly low numbers of imaging machines, hospital beds, urgent care clinics, etc. per capita, all well having administrative bloat that makes university administration look positively lean by comparison.
People love to fret about this politician or that politician, but the reality is that Canada got the incentives totally wrong because they sounded nice. No out-of-pocket expenses? No evil private medicine? No profit from healthcare!
As it turns out, central planning fails in healthcare just like it fails everywhere else. So "ensuring everyone has access to reasonably good healthcare" is an excellent goal, but "giving any level of government a monopoly on healthcare insurance" will be the death knell of the generally excellent healthcare Americans have access to if you have insurance.