There a number of ways to look at this issue, but the short version is that the House of Representatives, currently controlled by the Republicans (themselves now controlled by the Tea Party) are unwilling to in essence work any compromises with the Democratic controlled Senate or the President (himself a Democrat).  The Republicans have tied the raising of the debt limit to keep the government paying its dues to a larger political fight about the future of entitlements (e.g. Social Security, Medicare), taxes, the on-going recession, and the future of the US (which is currently on an unsustainable debt path).  

Meanwhile the immovable object that is the August 2nd deadline is coming head on with the irresistible force that is the Republican ideology against any and all tax increases.  There is an argument that the President can override the Congress by invoking the 14th Amendment. This would likely trigger a constitutional crisis (and potentially impeachment charges by the House Republicans) and a showdown in the Supreme Court.  

The alternative would be defaulting, having the credit rating of the US downgraded, and causing a massive double dip recession in the world economy.  

The commentator I have followed most closely and to me has been the clearest throughout this whole process is Jonathan Chait from The New Republic.

Herewith a big ol' mass of links from Chait to help understand this mess:

Obama Prepares for Stalemate

Bohner's Radicalism, Boehner's Dilemma   [John Boehner is the Speaker of the House]

Why It's So Hard for Republicans to Accept a Deal with Obama

What's John Boehner up to? 

Getting to No

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A couple of weeks ago I was at a party (the only American in a room of Canadians) and I (after a few beers admittedly) predicted I thought the US was 50/50 for defaulting.  I was told I was crazy that this would never happen.  I hope I still am proven wrong but I would say default is more like 75% at this point.  

* An important point with the graph above is the majority of the debt comes from George W. Bush's tax cuts to the riches plus two wars in Afghanistan and Iraq.  Obama then inherited the (so-called) Great Recession and implemented bailouts (begun under Bush) as well as the stimulus package.  The Republicans are now blaming him for creating this massive debt crisis though of course they were the ones in power when the bulk of it was created.  

Update I:  Also this piece by Matt Yglesias on misdirected fire at Obama.