Kevin Drum had an interesting post yesterday about a course change among Republicans in Congress. Even many members of the House Freedom Caucus, the farthest right group of Republicans in the House of Representatives, are saying they plan to vote for a budget resolution that calls for increasing deficits as far as the eye can see, climbing to over a trillion dollars a year a decade from now.
If the government spends more than it takes in, that's a deficit, and it makes up the difference by borrowing money, which adds to the national debt. As Drum says, the GOP has for the last few decades complained loudly about deficits and the debt when the president is a Democrat and largely tolerated them when he's a Republican.
Deficits exploded under Ronald Reagan and George H.W. Bush, for example. Then halfway through Bill Clinton's presidency the deficit turned into record surpluses and we started paying down the national debt so rapidly that the Congressional Budget Office projected it would be paid off entirely by 2010. (Clinton's budget surpluses were the first since Lyndon Johnson's final budget at the height of the Vietnam War, the War on Poverty, and the Apollo program.)
George W Bush's wars and tax cuts returned the country to deficits, which Vice President Dick Cheney famously defended by telling Paul O'Neill in 2004, "You know, Paul, Reagan proved that deficits don't matter." The financial collapse in 2008 led to emergency measures under Bush and Obama that exploded the deficit to over 1.4 trillion dollars in fiscal 2009 (roughly the last four months of the Bush administration and the first 8 months of Obama's).
A chart from mid-2011 summarizes the contributing factors that led to the deficit and debt explosion. Since then an improving economy, the Affordable Care Act (which actually reduced the deficit, something few people seem to realize), and constrained spending led to a much reduced deficit both in dollar terms and as a percentage of gross domestic product (GDP). For a more recent analysis from an independent source see this page.
Incidentally, expressing deficits in dollars can be misleading because it doesn't take into account inflation or the size of the economy. In nominal dollars the deficit was a lot smaller when George H.W. Bush left office than now, but the fiscal 1993 deficit was 3.9 percent of GDP versus 3.2 percent for fiscal 2016. (See this interactive chart from the St Louis Fed.)
So a projected trillion-plus-dollar deficit in fiscal 2026 needs to be considered in light of the size of the economy then. Unfortunately, it's unlikely GDP growth will be high enough to make up for 75 bigger deficit. But we can't have the massive tax breaks for the rich that Trump wants without increasing the deficit.
Updated 2016 January 9 to reference the actual fiscal 2016 deficit rather than the projected one for fiscal 2017 given the uncertainty of the latter and also to add a link to the interactive historical deficit graph from the St Louis Fed.