Chairman Powell has stated that he would not comply with a presidential request for his resignation, meaning President Trump would have to fire Powell if Trump was serious about removing him.
The law creating the Federal Reserve gives the president power to remove members of the Federal Reserve Board — including the chairman — "for cause." The law is silent on what does, and does not, constitute a justifiable cause for removal. So, President Trump may be able to fire Powell for not tailoring monetary policy to the president's liking.
By firing Powell, President Trump would once and for all dispel the myth that the Federal Reserve is free from political interference. All modern presidents have tried to influence the Federal Reserve's policies. Is Trump's threatening to fire Powell worse than President Lyndon Johnson shoving a Fed chairman against a wall after the Federal Reserve increased interest rates? Or worse than President Carter "promoting" an uncooperative Fed chairman to Treasury secretary?
Yet, until President Trump began attacking the Fed on Twitter, the only individuals expressing concerns about political interference with the Federal Reserve in recent years were those claiming the Audit the Fed bill politicizes monetary policy.