Would-be health reformers have long struggled with how much change American consumers and voters will accept. In 2008, Senator John McCain of Arizona, the Republican presidential candidate, experienced the dangers when he proposed a plan eliminating the tax break for employer-provided health coverage — and faced blistering “tax increase” attacks from Mr. Obama.

As president, Mr. Obama intended his program to limit the number of changes required. He grafted expanded coverage and changes in the individual insurance marketplace onto the existing system rather than building an entirely new one. He also left mostly undisturbed the much larger employer-provided insurance market, which currently serves an estimated 149 million people. “If you’re happy with it and your employer’s happy with it, keep it,” the president said at one point.

But Mr. Obama included a feature sure to make some employers less happy: To help finance his plan and constrain health costs, he reversed course and supported a new tax, beginning in 2018, on the most generous health care plans that some large companies provide.

Mr. Emanuel argues that this “Cadillac tax,” along with taxpayer subsidies now available for Americans with modest incomes, will expand and accelerate the trend away from employer-provided health care.

Even though the health law’s “employer mandate” requires that companies with 50 or more workers pay a penalty of $2,000 per employee if they do not provide health care, many large companies now spend far more than that to offer coverage. As a result, Mr. Emanuel says they will be able to pay the penalty, give workers a raise and shed the burden of providing coverage by sending workers to the public exchanges.

“By 2025, few private-sector employers will still be providing health insurance,” Mr. Emanuel writes in his book.

So far, his view remains an outlier among health policy experts. “There’s not going to be massive erosion” in employer-provided coverage, Mr. Gruber said. Similarly, White House advisers argue that large companies will continue to view health coverage as a crucial competitive tool for attracting the best employees. The Congressional Budget Office has projected a comparatively modest drop affecting three to five million people annually by 2019.