Newt resigned in early 1998 so, I doubt he was responsible.
"In the initial PAYGO regimen, enacted in the Omnibus Budget Reconciliation Act of 1990 (OBRA '90), by statutory requirement, any increases in the deficit were to be offset by an across the board "sequestration" of programs. This means an automatic cut in non-exempt mandatory spending programs -- this was calculated by the Office of Management and Budget at the end of the year.
These rules were in effect from FY1991-FY2002  and are widely seen as having assisted the US Congress in maintaining budget discipline. In FY 1991 the Federal deficit was 4.5% of GDP, by FY 2000 the Federal surplus was 2.4%.  Total Federal spending as a percentage of GDP decreased each and every year from FY1991 through FY 2000, falling from 22.3% to 18.4%. 
In 1998, in response to the first federal budget surplus since 1969, Congress started increasing discretionary spending above the statutory limit using creative means such as advance appropriations, delays in making obligations and payments, emergency designations, and specific directives.  While staying within the technical definition of the law, this allowed "emergency" spending that otherwise would not be allowed. The result was emergency spending of $34 billion in 1999 and $44 billion in 2000. In 2001 that amount jumped to $700 billion, most of which came from the 2001 tax cut (Economic Growth and Tax Relief Reconciliation Act of 2001).  In 2001 Congress began removing discretionary spending by statute from the PAYGO scorecard. Those amounts were $90 billion in 2001, $65 billion in 2002, $127 billion in 2003, $150 billion in 2004, $142 billion in 2005, and $444 billion in 2006. 
The appropriate change that should have been made to PayGo would have been to adopt a targeted surplus/deficit based on the state of the economy and to use that as the controlling limitation. With an economy growing in the 2-4% range, the target would be zero -- that is, no surplus or deficit. With a sluggish economy, a deficit would be appropriate with the size dependent on the condition of the economy. With an economy growing more than 4%/year, a surplus would be appropriate to prevent the economy from overheating. However, the reality was that when the PayGo program was first developed, no one believed that it would be possible to eliminate the deficit in any foreseeable future.
As noted in the Wiki quote, the "violation" pf PayGo rules was fairly minimal prior to 2001, with exemptions totalling around 30% of the actual surplus incurred in the budget. Under Bush, there was a much reduced surplus in the first year of the administration -- largely reflecting the final Clinton budget -- followed by massive and growing deficits thereafter in every budget proposed by the new administration.
The thinking that led to these deficits began at the top. Bush's first Treasury Secretary Paul O'Neill opposed a second round of tax cuts in 2002 because he believed that further stimulus was unwarranted and the cuts would result in a massive ballooning of the deficit. Cheney reportedly replied that "deficits don't matter" and forced O'Neill to resign a few months later (see, for example, http://www.washingtonpost.com/ac2/wp...nguage=printer). At the time of O'Neill's objections, it was clear that the inherited surpluses had been squandered and that the nation was headed yet again for massive deficits, obliterating the progress made during the prior ten years. O'Neill represented well the traditional Republican views of fiscal conservatism but found there was no room for him in a party which, on one hand believed that tax cuts would always generate growth offsetting revenue losses and, on the other hand, tended to believe that bankrupting government was the most efficient way to force a revolution against government spending. (See http://www.businessweek.com/magazine...4021_mz007.htm)
The Bush/Cheney policy was a sharp reversal of the policies advocated by Clinton, who was a fiscal conservative and often sought alliance with Republicans to counter Congressional Democrat efforts to spend more. People tend to forget that Clinton came to office as a member of the NDC, which was the equivalent of what are now called the Blue Dog Democrats, who are noted for being more fiscally conservative.
I do know Newt cut military retirement pay as part of his "contract with America" legislation.....not a very veteran-friendly stance there. But again, I'd rathe pay my fair share, than end up in the mess we're in today.
I'll be plenty happy to blame Obama if he continues the failed policies of the last administration, which so far, he seems to be doing. (and I don't include stem-cell research and gay marriage as existential crises facing our country)