It is absolutely ridiculous to blame the Democrat Party for the fact we do not have single-payer health insurance.
The Democrat Party is responsible for all the social welfare programs enacted in the 20th and 21st centuries; e.g., Social Security; expanding Social Security to spouses and dependents; disability insurance; unemployment insurance; a minimum wage; Medicare; Medicaid; the ACA; and expanding Medicaid under the ACA (in states controlled by Democrats).
Do you understand why there is no public option in the ACA? Three Senators (Nelson, D, NE; Lieberman, I, CT; and Landrieu, D, LA) all announced they would not vote for cloture if the bill contained a public option. Without a vote for cloture, bills are filibustered to death in the Senate, so even though a majority of Democrats were for a public option, Harry Reid had no choice but to bring a bill to the floor of the Senate without a public option. The Democrat Party is not monolithic and a few Senators can prevent a public option by using the filibuster. This is the tyranny of the minority.
We don't need a new party because we already have the Socialist Workers Party that supports socialized medicine (this is not single-payer; it is government ownership of health care or socialized medicine). The problem is that too many Republicans think socialized medicine is godless communism.