Indeed, and that is perhaps one of the two coherent claims made by republicans against a decent public options (single payer or otherwise).
Coherent Claim 1: The existence of a public option harms the viability and structure of a private option
Coherent Claim 2: A healthy, careful individual should not be forced to subsidize an individual who does not take care of their own health - but is forced to by a public option.
Both claims are a matter of opinion; It is my opinion that it is no different than police, school or war. (1: The existence of police harms private security; the existence of public schools harms private schools; the existence of the US army harms private mercenaries. 2: I should not be forced to pay for protecting someone who does not make an effort to protect themselves; I shouldn't be forced to subsidize teaching to anyone; I shouldn't pay for a war I didn't ask for).
I'm not sure why health care, which is sometimes (literally) a matter of life and death, and about which one has much less control than anything else, would not get a public option when schools do. And I have yet to find a republican who was coherent about why, if public healthcare is a problem, should we not also abolish police departments and public schools. But I guess one might exist.
The bigger problem with the republican standpoint, is that the coherent arguments aren't even made all that often; instead they tend to spread FUD with arguments that are easy to refute if you just care to look at examples - see, e.g. : http://news.ycombinator.com/item?id=4888507