By Eric Bradner and Tami Luhby, CNN

(CNN) -- Joe Biden is proposing massive new subsidies to make health coverage through Obamacare's exchanges cheaper -- as well as a new "public option" that would allow people to buy into a program his campaign says would be similar to Medicare.

The former vice president unveiled his health care plan Monday morning amid an escalating fight with his 2020 Democratic presidential foes as some more liberal candidates advocate enrolling all Americans in a national health plan, all but eliminating private health insurance.

Vermont Sen. Bernie Sanders is set to deliver a speech making his case for "Medicare for All" on Wednesday, according to his campaign. And California Sen. Kamala Harris, who has similarly backed a single-payer, government-run health program, teased the upcoming rollout of her plan in front of a crowd in New Hampshire on Sunday, too.

Biden, meanwhile, is pushing for a more moderate approach, built on former President Barack Obama's Affordable Care Act.

"We should not be starting from scratch. We should be building from what we have. There's no time to wait," Biden told an audience in Dover, New Hampshire, on Friday.

He said that under his plan, if "you like your employer-based insurance, you get to keep it." Under other leading Democrats' plans, he said, "you lose it, period."

Biden's plan would launch a "public option" that his campaign says would be "like Medicare," with primary care covered with no co-payments.

His plan leaves unclear some important details about how it would work, including how the plan would be administered and the rates at which doctors and hospitals would be paid -- which plays a crucial role in determining which health care providers would accept patients enrolled in the public option. But he promises to lower medical costs by negotiating lower rates with providers.

The public option would cover women's contraception and abortion, Biden officials said. Obamacare currently covers contraception at no cost. Abortion services are currently excluded from the 10 essential health benefits that insurers must cover. Insurers may offer coverage of abortions as long as they comply with the requirement to segregate federal funds.

Biden would also enroll nearly 5 million Americans who would have been eligible for Medicaid under Obamacare's expansion of the program -- but live in states that rejected that expansion -- in the public option, for free.

And he would take a series of steps designed to lower the cost of purchasing insurance on Obamacare's exchanges by providing federal subsidies for everyone, regardless of their income.

Currently, only those who earn less than 400% of the federal poverty level -- or about $100,000 annually for a family of four -- qualify for help paying their premiums. Biden would lift that cap.

Also, those enrolled in an Obamacare plan would have to pay no more than 8.5% of their income -- instead of the current 9.86% -- in premiums. A family of four earning $110,000 annually would save about $750 a month in premiums, the campaign said.

And he would base those subsidies on the cost of "gold plans," which have higher premiums but lower deductibles, rather than less generous "silver plans." That means people could spend less money out of pocket -- or could use the larger subsidies to buy less expensive silver or bronze plans. This move would help address a major criticism of Obamacare -- that its deductibles are too high. The average deductible for an enrollee under Obamacare in a "gold plan" is just under $1,600 in 2019, while for a "silver plan," it's just over $4,000, according to the Kaiser Family Foundation.

Biden's campaign characterized the proposal as a return to what Obama had originally sought in 2009, when he unsuccessfully lobbied the then Democratic-run Congress to include a public option in the law.

"We're starting with the Affordable Care Act as the base and going to insist on the elements that we sought last time -- and we'll get them this time," a senior Biden campaign official said.

Biden's plan also aims to curb prescription drug prices, including allowing Medicare to negotiate prices with drug makers. Also, the prices of newly launched drugs that face no competition would be the subject of a review by an independent panel established by the Health and Human Services Department, and, in certain cases, recommend reasonable prices based on the average price in other countries. People would also be allowed to import some prescription drugs from other countries, and drug makers would face tax penalties for increasing the price of their brand-name, generic or biotech drugs by an amount larger than the inflation rate.

Biden's proposal would carry a price tag of $750 billion over 10 years, his campaign said. He is proposing to foot the bill by raising income taxes on the wealthiest Americans to 39.6% -- reversing part of the Republican-led Congress' 2017 tax cut law that reduced that rate -- and by requiring those who earn more than $1 million per year to pay 39.6% taxes on capital gains, rather than the current 20%. The federal government will spend an estimated $58 billion in 2019 on subsidies related to the Affordable Care Act, according to the Congressional Budget Office.

Biden's plan does not include any contingencies that would kick in if federal courts currently considering a legal challenge to Obamacare strike down the law, in part or in full.

"We are moving forward with the expectation that it will continue to be (upheld), and he's going to continue to fight to build on it and expand on it," a senior campaign official said.

While Biden is painting his plan as more achievable than Medicare for All, Sanders stood his ground, tweeting a few hours later that he fought to improve and pass Obamacare.

"I traveled all over the country to fight the repeal of Obamacare," Sanders said in a tweet that included a video of Obama calling Medicare for All a good new idea. "But I will not be deterred from ending the corporate greed that creates dysfunction in our health care system. We must pass Medicare for All."