To answer this question, one must first ask: what is the Republican party and who leads it?
There are three possible answers to these questions. Here is a helpful distinction political scientists invented a while ago. There is the party in the electorate consisting of rank-and-file Republican identifiers, there is the party as organization instantiated in the DNC,and there is the party in government, which is the sum of elected Republican officals in government. So here are the potential leaders of the Republican party:
Leader of the party in the electorate - Rush Limbaugh, or so he hopes.
Leader of the party as organization - Michael Steele, or so he tries.
Leader of the party in government - future nominee, or so s/he plots.
Rush Limbaugh's recent elevation in the political limelight was a result of the fact that the Republican party in government is in shambles after a stinging defeat in the 2008 elections. (It wasn't just because President Obama mentioned him in a speech.) John McCain has been sidelined, and no one (not even Bobby Jindal, especially after his much derided reponse to the president's message to a joint session of Congress) has emerged to fill the political vacuum on the Right. The party in the electorate are yearning for a shepherd and since they are not finding it in government, they are looking to a talk-show host.
The recent tussle between Limbaugh and Michael Steele was only to be expected in the light of this threefold characterization of the Republican party. They were merely jostling for power as the party in government is regrouping. But it also tells us how weak parties have become as personalities (in the media and in politics) have trumped organizations in the running of American democracy.
None of this is good for the Republican party (as organization). When the party in the electorate has to turn to a talk how host for a potential leader, it spells disenchantment at their elected representatives in DC. The organization - its fundraising and voter turnout machine - was what gave the Republicans the electoral edge up till 2006. But now the party appears to be left only with personalities - like Joe the Plumber (still around), Aaron Schock (the youngest member of Congress), and Limbaugh. Personalities flit in and out of political life, and at best can only temporarily bring together a a diverse coalition of interests. They are not the way back to a competitive two-party system.