Yes, vouchers have been not only proposed but experimented with in Connecticut and a few other places. Often forgotten are the arguments made by Steve Forbes (who?) for them:

"Replace “gatekeepers” with health care vouchers

The key is putting patients in charge of health care resources again. There’s no need for all of these 3rd parties, HMO’s, insurers, employers, gate keepers, government bureaucracies that stand in the way. [You should] have your choice of several hundred different health care plans. If you need long-term care [or] prescriptive medicines you can choose a plan that does it. And for those on Medicaid, you should be able to have vouchers so you make the choice, not where the government tells you to go.

Here is one sweeping proposal from Robert Blandford that combines a Federal Single Payer system with vouchers and medical savings accounts  (An Approach to National Health Care: Lifetime Voucher, Single Payer, and Mandatory Medical Savings Accounts, January 19, 1998)

SUMMARY

"(1) Each person would be given a fixed, non-transferable, dollar amount (e.g. $25,000-$50,000) inflation-indexed health care voucher at birth. Preventive care would be encouraged by a yearly use or lose voucher for $150 ... . Wage earners would be required to fund mandatory MSAs at 5% of income up to a minimum of $1000/year if possible, and a maximum of $4000/year, until their contributions plus the MSA earnings reach $100,000 if possible. MSA contributions, and earnings would be treated as regular income for tax purposes. The voucher, since it is an entitlement, would not be treated as income when spent. The MSA and voucher could be spent only on medical care, and procedure payments would be at or below the 50th percentile in the region of the provider, see (4). All the MSA, and a fraction of the voucher, perhaps one-third, can be transferred to a person's estate at death. ...

 Although the voucher/mandatory MSA is implemented within a single payer type system, the single payer does not control costs; see (4) and (6) below. There is very little rationing before the voucher/MSA is exhausted, see (9). For a discussion of the appropriateness of the government-provided $25000-50,000 see (31). Providers may charge any amount, each person can have costs up to the 50th percentile paid with his voucher/MSA for any provider, and the induced strong competition reduces costs. Program initiation is discussed in (19).

The voucher/MSA may be used to purchase private health insurance, see (10). It is hoped that persons would use their voucher/MSA for non-catastrophic expenses in preference to purchasing comprehensive insurance, thus building a large free market for most procedures. If comprehensive insurance is largely unregulated the initial tendency will likely be for the healthy not to purchase it. The resulting adverse selection will drive up the cost of comprehensive insurance leading in turn to fewer purchasers. This will not lead to ill health for the sick because the voucher and MSA enable patients to obtain care up to the catastrophic limit of their catastrophic policy.

Just as MSA premiums and earnings are treated as regular income, private insurance premiums and other health expenses are not tax-deductible. Persons may pay providers directly to avoid spending down their voucher/MSA, see (12). The budget may be balanced automatically each year by a mechanism which is possible only in the context of a fixed lifetime voucher, see (16).

From a political point of view the voucher could be regarded as a "Democrat" addition to level the MSA playing field for the poor."