The data backing this claim up are pretty solid. The most widely-used measure of political polarization, a score of ideology based on voting developed by Kenneth Poole and Howard Rosenthal, has shown that the Republicans in the Senate and especially the House have drifted away from the center far more rapidly than Democrats. The chart below, taken from the most recent slice of their data released just last month, illustrate this pretty clearly:
Right around 1975, the Republican party sharply turned away from the center line and hasn't looked back. The Democrats have been drifting away from the center too, but nowhere near as quickly.
Every once in awhile an op-ed writer will come along and make a qualitative argument along the lines of "no, really, it's the Democrats who are polarizing!" Peter Wehner, a former official in three previous Republican presidential administrations, did just that in the pages of the New York Times last week. His argument amounts to the notion that since President Obama has pursued some policies that are more liberal than Bill Clinton's, "the Democratic Party has moved substantially further to the left than the Republican Party has shifted to the right."
Well, no -- just look at the chart above! Here's another way of looking at it: How many moderates are in each party? Here's another interesting chart from the Poole-Rosenthal data, showing the number of House members in each party who are not centrists -- that is, whose ideological scores put them on the more extreme ends of the partisan scale.
As you can see, in the most recent Congress nearly 90 percent of Republican House members are not politically moderate. By contrast, 90 percent of Democratic members are moderates. It's quite difficult to square a chart like this with a claim that Democrats are abandoning the center faster than Republicans. As the chart shows, there are plenty of centrist Democrats left in the House -- but hardly any centrist Republicans.
It's worth pointing out that none of this is happening in a vacuum -- House Republicans are become more extreme because Republican voters are electing more extreme candidates. We see many of these same patterns playing out among the electorate as well, as a massive Pew Research Study demonstrated last year.