The Congressional Budget Office has estimated that if the mandate were to be repealed, 13 million more people would be uninsured by 2027 than are currently projected.

The mandate currently requires most Americans to have some form of health coverage during the year or pay a tax penalty.

The groups, in a letter to Congressional leaders, said, "Eliminating the individual mandate by itself likely will result in a significant increase in premiums, which would in turn substantially increase the number of uninsured Americans."

"As providers of healthcare and coverage to hundreds of millions of Americans, we are committed to assuring everyone has access to a range of high quality, affordable coverage options so they can access the care they need, regardless of pre-existing conditions," said the letter from the health industry groups.

"To achieve this critical goal, we are urging you to maintain the individual mandate unless and until Congress can enact a package of reforms to adequately assure a balanced risk pool and prevent extraordinary premium increases."

The letter was sent by America's Insurance Health Plans, the BlueCross Blue Shield Association, the American Medical Association, the American Academy of Family Physicians, the American Hospital Association and the Federation of American Hospitals.

Shortly before the letter was released, Senate Republican leaders announced that their new tax reform bill would seek repeal of the individual mandate.

Repealing the mandate would give the Republicans almost $340 billion in budget savings that could then be applied to tax cuts.

The savings would result from the government having to subsidize fewer Obamacare customers' premium payments. Under the Affordable Care Act, low and middle-income Obamacare customers qualify for federal tax credits that reduce their monthly premiums.

Republicans had called for repeal of the mandate as part of prior bills this year that sought to gut major parts of Obamacare and replace them with other provisions.

Those bills all failed to pass after a handful of Republican senators, concerned about potential losses of health insurance coverage by millions of people, refused to vote for them.

The bills were broadly unpopular among the American public. Last week, a sweeping series of victories in Virginia state elections by Democrats was credited in part to the issue of health care, with voters more in favor of retaining the Affordable Care Act than opposed to it.

The Protect Our Care Campaign, an Obamacare-defense group, cited those results Tuesday as it criticized the Senate bill.

"It was exactly one week ago today that voters across the country sent a clear message rejecting the Republicans' partisan health care repeal agenda, and yet here we are again," said Brad Woodhouse, director of the Protect Our Care Campaign.

"After repeatedly failing to repeal the Affordable Care Act, of which their legislation was the least-popular bill in three decades, Republicans are apparently trying once again to jam a partisan repeal down the throats of the American people to pay for tax breaks for the wealthiest individuals and corporations.

"Make no mistake, repealing the individual mandate is tantamount to repealing the Affordable Care Act, and as such it would be wise for those few Republicans in the House and Senate who said 'no' to previous efforts at repeal to say 'hell no' to this one," Woodhouse said.