If we implement it like the Scandinavian countries, the average poor family would still have to pay 600-700 per month. I believe that would be about 2/3 of her monthly income.
The Scandinavian implementation is not the only option; although it would still be an improvement. ~$700 is about what people pay for 'Bronze' plans before their deductible. For someone with a chronic condition, the average out-of-pocket would be much higher to access any amount of care.
Alternatively, the Canadian system does not require any sort of insurance-like payment to access all but a few parts of the healthcare system. While wait times are a bit of a problem for non-emergency care, Canada pays ~1/3rd of what America pays for healthcare. That leaves significant funding available to improve on that system simply through more doctors and and better equipment availability, while still being much more cost-effective than the current system. It should also be extended to dental and drug insurance, but again, there is ample funding available to accomplish that and still remain cheaper than the current system.
Medicare For All is most similar to the Canadian 'insurance', and the best candidate for healthcare reform. There are some important conditions for it's success however---the restrictions on price negotiation must be removed; equivalent private insurance must not be allowed; and taxes must be increased to appropriately fund the system. Ignoring any of these will allow the system to be corrupted by wealthy interests (of HN includes many), and could result in a system deliberately designed to fail. Rich people _must_ use the same healthcare service as poor people, aligning incentives among all socio-economic classes, ensuring the system remains effective and well-funded.
No they wouldn't, taxes don't just pay for healthcare in Scandinavia it also pays for free daycare, free college and a year of state paid parental leave.