"It was a similar situation as we have now. We had a Democratic president who had lost his majority -- in that case -- in Congress in general, in this case in the House," said Alan Auerbach, director of the Burch Center for Tax Policy and Public Finance at the University of California, Berkeley. "In both cases you had a Republican leadership in the House that felt it had a very strong mandate and wanted to take a divergent path from the White House."
There's also the Tea Party's influence. Many of its leaders are calling for a government shutdown to send a signal to the Obama administration. That is a challenge for Republican leaders, who walk a fine line between challenging the president on spending and looking as if they are letting government services come to a halt.
In 1995, the Republicans, led by then-House Speaker Newt Gingrich, took much of the public blame and suffered a major political setback.
Gingrich's disapproval rating surged to 65 percent during the budget battle with Clinton, while the president's own approval rating surged to 53 percent, the highest it had been in two years, according to a Gallup poll.
In today's climate, both parties, and Obama, are likely to take the blame.
"In 1995, the Clinton people succeeded very well in making that government shutdown look like an act of petulance by Newt Gingrich," Gleckman said. "The Clinton people were masterful at that. I'm not sure that Obama either has the political skill or the interest in playing that kind of a game."
The debate highlights vast political and ideological differences over the federal budget. Congress last year failed to come together on a 2011 budget and has been operating on the 2010 budget, funding government through continuing resolutions that need to be extended every few months.
Lawmakers narrowly averted a shutdown at the end of last year and the lack of resolution on a budget has stalled several research projects and new initiatives.
Democrats and Republicans are likely to come together eventually on a budget to avoid public backlash, but it is likely to happen after much political drama.
"Whatever got us here is a big poker game," Gleckman said. "They are going to play out this hand of poker until the last card, and I suspect in the end they will come to some agreement."