Federal Reserve officials are showing scant support for what would be the most drastic single policy tightening in almost three decades, though they're on board with a series of still-large moves aimed at curbing an inflation spiral.

Chair Jerome Powell and other officials haven't backed a suggestion by their St. Louis Fed colleague James Bullard to consider the first 75 basis point (bps) hike since 1994. But their remarks—which endorsed a 50 bps increase next month and at least one more such move to curb surging prices—were sufficiently hawkish to send U.S. stocks reeling.

"I would support at this point, given where the economy is, a 50 basis point rise in May, and a few more to get to that 2.5 percent" level by the end of the year, Cleveland Fed President Loretta Mester told CNBC on Friday afternoon, referring to the neutral rate that neither speeds up nor slows down growth. "Doing one outsized move in the funds rate doesn't appear to me to be the right way to go. I would rather be more deliberative and more consistent."