Evidence from history is that fiscal policy is FAR stronger than monetary policy. Ask any serious macroeconomist. The Fed actually can't counteract a sufficiently large fiscal policy, though they sometimes try. (A sufficiently extreme fiscal contraction policy certainly can't be countered by the Fed because the Fed can't lower interest rates significantly below 0%. On the other side, a very large fiscal expansion policy will swamp any efforts by the Fed to raise interest rates, as private lending will undercut the Fed rates.)
(Historical examples of the Fed trying to counteract fiscal policy are mostly of a Republican-led Fed trying to counteract pro-growth fiscal policy during a depression, which is sort of nasty.)
Oh, and you CAN fight the Fed, if you're big enough. Soros fought the Bank of England and won, remember?
Why is fiscal policy stronger than monetary policy?
Answer #1: because monetary policy is mere *loans* -- they increase people's supply of cash without increasing their wealth, and due to the interest charges, often decrease household wealth. Fiscal policy is *payments for services*, which increases people's wealth *and* their supply of cash. This is a critical difference: this is why monetary policy can walk the country into a household-debt trap, while fiscal policy cannot.
Answer #2: monetary policy has a bad transmission channel: the Fed lends to the banks, who probably just sit on the money (this is what happened in 2009) or lend it to their buddies. Fiscal policy goes directly to pay workers, with a much more immediate economic result. (Of course, if the fiscal policy is tax cuts for billionaires or sweetheart contracts for Lockheed Martin executives, it's not nearly as effective as it is if it's health care or public services or direct payments -- such as G W Bush did -- for all Americans.)
