There's been two health care news stories that have gotten some attention in recent days.
The first one is that the cost of family health coverage in the U.S. now tops $20,000 a year for the first time ever.

Fewer Americans under 65 had employer coverage in 2017 than in 1999, according to a separate Kaiser Family Foundation analysis of federal data. That’s despite the fact that the U.S. economy employed 17 million more people in 2017 than in 1999.

The other story is that the number of Americans without health insurance jumped by nearly 2 million in the past year.

Tom Miller, a resident fellow at the American Enterprise Institute, a conservative think tank, said the drop in Medicaid coverage “is a positive.”

“When the economy grows Medicaid eventually drops,” he said.

One reason for the drop in health coverage is that middle-income families can’t afford the rising cost of insurance in the individual market, particularly if they don’t qualify for government subsidies, he added.

Yeh, that doesn't make much sense. Even if it's true, that still sounds like polishing a turd.
Secondly, research studies contradict this claim.

There is no relationship between changes in states’ Medicaid and CHIP enrollment and changes in their unemployment rates over the March 2017-March 2019 period. In other words, the states with especially sharp enrollment declines did not have especially sharp unemployment declines. If anything, there is a slight negative relationship between enrollment changes and unemployment-rate changes.
...
818,000 (2.3 percent) fewer children were enrolled in Medicaid or CHIP in March 2019 than two years prior.. What has received less notice is that Medicaid enrollment among adults also fell by 750,000 (2.1 percent) over this period

No time in the last 40 years has been such a large decline in Medicaid and CHIP enrollment, and there is no correlation between employment and enrollment.
However, there is a correlation between enrollment and Medicaid work requirements in Republican states.

LePage’s administration argues that the work requirement will help people earn more and become more self-sufficient. But according to Hannah Katch, a senior policy analyst at the Center on Budget and Policy Priorities and a former administrator of the California Medicaid program, 80 percent of Medicaid patients nationwide are already in working families. “The vast majority of people who aren’t working are either taking care of a family member, have a physical or behavioral health condition, or are in school, or have a combination of these factors,” said Katch. “While a work requirement is unlikely to help them get a job, it is very likely to take away health coverage from people who can’t work.”

Arkansas was one of the first states to impose work requirements for Medicaid.
A study of the program there revealed that nearly three-quarters of people kicked off of Medicaid became uninsured and remained so until the end of the two-year period.
"Lack of awareness and confusion about the reporting requirements" were the normal reasons found for people not meeting the requirements.
President Trump’s latest budget called for $1.5 trillion in cuts to Medicaid. Trump’s lawsuit to fully repeal the Affordable Care Act would end Medicaid expansion.