We have single payer health insurance in the US. It's called Medicare, among the the most successful and popular government programs ever established. As with the ACA, conservatives, including, famously, Ronald Reagan, decried it as socialism, and predicted it would destroy the country. Like the ACA, it had an awful roll out. Finally like the ACA, it's a program in which the young and healthy subsidize the old and sick Along with Social Security, it dramatically reduced poverty among the elderly. It is far more efficient than private insurance.
Now, you're welcome to criticize Medicare on conservative or libertarian or philosophical grounds. You're even more welcome to agree with me that Medicare is unsustainable in its present form and as such in deep need of reform. But I would caution you about the politics of being against Medicare. As even the most "conservative" (or is it actually hypocritical?) Republican legislators understand, Medicare is as sacrosanct to Tea Party members as it is to liberal Democrats.
Maybe that's why the Right so loathes Obamacare. It just might work....like Medicare.