Yes. Bill Clinton governed as a moderate Republican because countless opinion polls and sh!tty advisors told him he had to.
Clinton's quote on the budget (as opposed to with Dick Morris later on in 1995/1996, which I think has developed into something of a myth) was 'we are Eisenhower Republicans against Reagan Republicans. We stand for the bond market and for balanced budgets.' He was complaining that the "investments" he and Robert Reich wanted (like what passed under President Biden) had to be stripped out of the 1993 and future budgets in order to achieve $500 billion in deficit reduction over five years.
Unfortunate, but the bond markets (and foreign exchange markets) tend to exist in the 'reality based community' and, after all, were what brought down Liz Truss and her fantasy tax cuts for the wealthy budget.
On Dick Morris, the 1990s was a very right wing era and Clinton himself had campaigned on welfare reform in 1992.
The myth making is that Dick Morris had Clinton agree on all sorts of right wing legislation with the Congressional Republicans. He wasn't around a long time before he started to make all sorts of wild claims about what Clinton was going to do with the Congressional Republicans, to the point where even centrist to right leaning Democrats like Clinton's then Chief of Staff Leon Panetta started to tire of him, and seemingly entirely forgotten is that Clinton also extracted major concessions for Democratic legislation in return from the Congressional Republicans.