The GOP War budgeting: when did start, and which pols got the ball rolling?Another good question.
To link back to some earlier stuff...I suppose it goes back to Ronald Reagan and Newt Gingrich. Reagan, because when confronted with policies that added up to bigger budget deficits even though he was a longtime anti-deficit crusader, he was capable of believing that nothing had changed in his positions. And Newt, because he believed in using words that polled well or focused grouped well regardless of whether they had anything to do with underlying policies. And, substantively, because Reagan's flip to embracing supply-side tax cuts and then Newt's role in cementing anti-tax extremism within the party made it necessary to play word games (knowingly or not) in order to remain dedicated to "balanced budgets." I might look, too, at the Ross Perot campaigns, which were extremely heavy on budget deficit talk but entirely empty of deficit reduction planning, other than to automatically oppose any plans that were out there.
Some Republicans during the Bush years played with the notion of giving up the budget rhetoric (Dick Cheney gets cited a lot), but it didn't take, at least for now. I'm not sure, however, whether the real collapse into a war on budgeting comes from the 1980s, the Obama years, or some time between them. If I wanted to research it, I might look at the rhetoric surrounding the George H.W. Bush budget deal and then the Clinton budget package in 1993.