In South Carolina, Republican Sen. Lindsey Graham has been attacked in television ads for his support of immigration reform. In Tennessee, GOP Sen. Lamar Alexander is ducking criticism from Tea Party groups that his overall voting record is too moderate. Kentucky’s Mitch McConnell, the Senate Republican leader, faces angry conservatives in his state for not joining an effort by some in his party to block the federal budget unless it defunds Obamacare. For these Republicans, the only uniting factor is that the criticism is coming from their own party. The reasons they are under attack vary from one group to...