I view the source of this "pushback" as coming mainly from political Libertarians of the Right. (These people would do well to consider that they are in the same political compass quadrant as was the contemptible modern-day philosopher and cult leader Ayn Rand.)
One way to achieve "price stability" would be through direct authoritative government price controls. Perhaps the latest attempt by the US government to use this policy option was during the Nixon Administration so I have been looking for information about what the debate was back then, to perhaps learn something from that part of economic history.
The concept of government price controls is universally condemned by the political right, and not even considered by the political left; so this should be a tip-off to the heterodoxy that this should be looked into further; "The enemy of the moron is my friend".
It often seems to me that the JG part of MMT is a situation where the government is to an extent "controlling" or setting the price of labor, and letting the quantity of that labor that is supplied by the non-government "float", depending on how many people report to the JG. Not so much a human "buffer stock", which I view as a somewhat insensitive term, but rather, people responding to the need to obtain balances of the currency in view of fiscal policy and non-government sector savings desires, both foreign and domestic.
So as to economic policy machinations, playing off the twin concepts of "price stability" vs employment, within the Nixon Administration, I found this write-up at PBS which if accurate is perhaps revealing. Some excerpts:
...confidence had risen in the ability of government to manage the economy and to reach out to solve big social problems through such programs as the War on Poverty. Nixon shared in these beliefs, at least in part. "Now I am a Keynesian," he declared in January 1971 -- leaving his aides to draft replies to the angry letters that flowed into the White House from conservative supporters. He introduced a Keynesian "full employment" budget, which provided for deficit spending to reduce unemployment.
"He attributed his defeat in the 1960 election largely to the recession of that year," wrote economist and Nixon advisor Herbert Stein, "and he attributed the recession, or at least its depth and duration, to economic officials, 'financial types,' who put curbing inflation ahead of cutting unemployment." The administration remained overtly dedicated to markets. But there were those in it who believed that the "market" was more an idyll of the past than an accurate description of how the current economy functioned.It's short and perhaps it will help us remember that there once was a time when people in the government were not afraid to seize the reigns of authority and simply make things happen.