They are not moderate Republicans, they are Assistant Democrats, Bush included.
I put “moderate” in quotes like that for a reason.
Essentially they are spendthrift progressives who may for partisan reasons resist spending when a Democrat is in the White House ... or rather used to, the jury is still out on that ... but who worked with Democrats to spend freely when a Republican is in the White House.
Actually, they think of Democrats as friends rather than enemies no matter who has been in the White House.
The “moderates” felt their oats very early in W’s tenure, you may recall Jumping Jim Jeffords back stabbing the country for example.