Unless you signed something to the contrary, the hospital bill is most likely an unpaid debt, rather then a breach of contract.
This answer is offered for informational purposes only. It is not offered as, and does not constitute legal advice or create an attorney client relationship.
The answer depends on how the initial pleading is drafted.
The debt itself is not one or the other; the real concern is under what legal theory the law suit against you would be filed.
If a statement or invoice is attached to the pleading, the allegations may assert an open account, an account stated, and, if the nature of the services rendered are shown in the statement, goods and services rendered.
Don't forget, you probably signed all kinds of papers when you were admitted to the hospital. It is very possible that language in the admissions forms--and they sure put a lot of paper in front of you, don't they---contains language by which you obligated yourself to pay the hospital's charges. That would be a contract and enforceable as such.
The statute of limitations that is applied will depend on what is included in the initial pleadings. If they just attach a statement or invoice, then the suit is on an open account or an account stated. If they attach a document which you signed in which you acknowledged the obligation to pay the charges, then the suit is on a contract. The pleading may list all 3 of those actions, and then another for services and goods rendered.
Under Federal law, specifically, the Fair Debt Collection Practices Act, it is unlawful for an attorney to bring suit on a claim that is barred by a statute of limitations. However, that law does not apply to the creditor itself.
Unless you have kept all the documents you received from way back when, you won't know what language was contained in the documents you signed. That creates uncertainty in terms of how you respond to collection efforts.