No the Republicans are NOT fiscally responsible. Due to their votes in congress the U.S. is now officially insolvent. We are paying $one trillion a year, just on interest. Let that sink in.
This disastrous situation came about due to giving corporations and billionaires huge tax cuts (which they used almost entirely for stock buy-backs.) This was grossly irresponsible policy.
Also, hugely excessive defense spending. If we want to have a billion dollar a year defense budget we simply have to pay for it, up front with taxes.
Our huge federal deficit is entirely the fault of the Republicans.