Now, the insurance industry is firing back and some advocates are protesting the change. Some say it goes too far, others argue not far enough. And the battle lines over the question of a mandate may make for some odd bedfellows in the weeks ahead. Many Democrats and Republicans are in favor of the change, albeit for different reasons.
At the same time, the insurance industry finds itself agreeing with some liberals who argue the requirements won't be meaningful enough to make sure that young and healthy people purchase insurance.
Under the bill, individuals and families will be required to buy health insurance, and will pay a penalty if they don't. In the original version of the bill, that penalty topped out at $950 per family; in the new version the fee won't exceed $750.
Also, under the amendment the penalties do not start until 2014. That year, the top penalty will be $450 and it will gradually rise to $750 by 2017.
The amendment also expanded by an estimated 2 million the number of people who would be granted a "hardship waiver" exemption. Under the original bill, anyone whose health coverage would cost more than 10 percent of their income would receive the waiver; the amendment lowered that threshold to 8 percent.
Conservatives largely oppose an individual mandate on principal, arguing that it is unconstitutional to force Americans to buy insurance that they don't want.
Meanwhile, many Democrats support a mandate as the best way to expand coverage and reduce overall healthcare costs. But many say the Finance Committee's legislation doesn't offer enough subsidies to make insurance affordable to low-income families and penalize people for failing to buy what they can't afford.
That's the reason given by Sen. Charles Schumer, D-N.Y., one of the co-sponsors of the amendment with Republican Sen. Olympia Snowe of Maine:
"If you have to make a choice when there are limited dollars, it seems to me this is the best choice," Schumer said, according to Kaiser Health News.
The debate over penalties illustrates the current tug-of-war between keeping the cost of health care reform legislation down and expanding access to coverage, says Urban Institute health policy researcher Linda Blumberg.
Blumberg believes that an individual mandate is a key component of health care reform. In an editorial this summer in the New England Journal of Medicine, she argued that a mandate was the most feasible route to universal health coverage in the U.S., and that to be effective, it would have to include significant penalties for failing to comply.
That's because if people are allowed to choose whether to purchase insurance, those who are young and healthy will be less likely to do so. That will leave the sick and elderly dominating the insurance pool, and so everyone's costs will go up. If young, healthy people are required to participate, it will spread the cost around.
But, Blumberg says, the government must also provide enough subsidies to low-income people to make coverage affordable -- something she believes the Baucus bill falls short of.
"If you're going to peel back the subsidies, then fairness dictates you have to let some people out," she says.
Insurance companies, who stand to benefit from an expanded customer base, are squarely on the side of stricter penalties.
A new analysis released by the industry Monday - and commissioned by the industry from the accounting firm of PriceWaterhouse Coopers - argues that weaker penalties are one reason why premiums would rise thousands of dollars higher than projected.
But a preliminary estimate by the Congressional Budget Office last week estimated that the finance committee bill -- with the new, weakened penalties - would help lower overall costs and cover 94 percent of American citizens up from 83 percent now.
Costs for individuals - and the overall long-term costs for the system - are expected to continue to be a central sticking point of the negotiations in the days ahead.
The Senate Finance bill is one of five bills pending in the House and the Senate that contain different requirements for buying insurance. And those differences will have to be resolved before any legislation makes its way to the president's desk.
---- Compiled by Lea Winerman, Online NewsHour