"This is not government-run," Clinton said of her plan to extend coverage to an estimated 47 million Americans who now go without.
All Americans would be required to purchase health insurance, reports CBS News chief White House correspondent Jim Axelrod.
Businesses would have to offer insurance to employees or pay into a pool for the uninsured, and no insurance company could refuse anyone coverage because of pre-existing conditions, adds Axelrod.
Clinton would also offer a tax subsidy to small businesses to help them afford the cost of providing coverage to their workers.
She put the government's cost at $110 billion a year.
"Perhaps more than anybody else I know just how hard this fight will be," said the New York senator.
Dismissing the inevitable Republican criticism, Clinton admonished the crowd. "I know my Republican opponents will try to equate health care for all Americans with government-run health care. Don't let them fool us again. This is not government-run."
A front-running contender for her party's nomination, Clinton drew criticism this time from fellow Democrats as well as Republicans.
"To ensure all Americans have affordable health care will take more than leadership that simply knows how to fight," said rival Sen. Chris Dodd, D-Conn.
Addressing a crowd at a medical center in the early voting state of Iowa, Clinton laid out her proposal, with the centerpiece a so-called "individual mandate," requiring everyone to have health insurance - just as most states require drivers to purchase auto insurance. Rival John Edwards has also offered a plan that includes an individual mandate, while the proposal outlined by Barack Obama does not.
"I believe everyone - every man, woman and child - should have quality, affordable health care in America," said Clinton, vowing to accomplish the goal in her first term.
For individuals and families who are not covered by employers or whose employer-based coverage is inadequate, Clinton would offer expanded versions of two existing government programs: Medicare and the health insurance plan currently offered to federal employees.
Consumers could choose between either government-run program, but aides stress that no new federal bureaucracy would be created under the Clinton plan.
Clinton proposed several specific measures to pay for her plan, including an end to some of the Bush-era tax cuts for people making more than $250,000 per year. Edwards has vowed to completely repeal the tax cuts for high earners to pay for the cost of his plan, estimated at $90 billion-$120 billion per year, while Obama would pay for his plan in part by letting the tax cuts expire in 2010.
Her speech came nearly 14 years after her first attempt at a universal healthcare plan that was highly criticized by Republicans as a socialized medical plan that eventually fell apart and left a stain on the former First Lady's record, reports CBS News reporter Fernando Suarez. Despite her failed attempt in 1993 Clinton assured the crowd of about 150 doctors, nurses and patients that she grew from her experience.
Aides say she has jettisoned the complexity and uncertainty of the last effort in favor of a plan that stresses simplicity, cost control and consumer choice.
In response, Obama said Clinton's plan is similar to one he proposed in the spring, "though my universal health care plan would go further in reducing the punishing cost of health care than any other proposal that's been offered in this campaign."
He took another swipe at the Clinton administration's closed-door sessions on health care in the 1990s, saying "the real key to passing any health care reform is the ability to bring people together in an open, transparent process that builds a broad consensus for change."
Other Democratic rivals were swift in their criticism.
Delaware Sen. Joe Biden said, "If universal health care plans could have gotten us health care, we would have gotten it a long time ago." Added John Edwards: "If you're going to negotiate universal health care with the same powerful interests that defeated it before, your proposal isn't a plan, it's a starting point."
Edwards said on his first day in office he will submit legislation that would pull health insurance for the president, members of Congress and all political appointees unless they pass universal health care within six months.
Republican Mitt Romney, in New York City for a fundraising stop, criticized Clinton's proposal, saying, "'Hillary care' continues to be bad medicine ... in her plan, we have Washington-managed health care. Fundamentally, she takes her inspiration from European bureaucracies."
The plan that Romney helped institute while governor of Massachusetts requires the same individual insurance mandate as Clinton's and uses state subsidies to help reduce the cost of private coverage. Since then, Romney has said he would leave it up to the states to decide whether they supported such a mandate.
Said Republican Rudy Giuliani's campaign: "Senator Clinton's latest health scheme includes more government mandates, expensive federal subsidies and more big bureaucracy - in short, prescription for an increase in wait times, a decrease in patient care and tax hikes to pay for it all."