By Martin Baccardax Updated at 2:17 pm EST The Federal Reserve was worried that inflation may become so intrenched in the U.S. economy that the public would question its resolve to fight it, minutes of its June policy meeting revealed Wednesday, while officials argued for the need for more rate hikes over the coming months. The minutes indicated that a larger-than-expected rate hike was needed in June in order to tame the fastest inflation in four decades, noting that the outlook for consumer price increases had deteriorated leading up to the June 15 decision. The Fed lifted its base lending r…