Republicans say they intend to do everything they can to make a campaign issue out of efforts by the White House to push Democratic Rep. Joe Sestak out of Pennsylvania's Senate primary, as the Obama administration continued to face questions Tuesday over the legality of its actions.

The Republican National Committee said it will highlight the issue via Twitter, online video clips and e-mail blasts to reporters ahead of November's midterm elections, while the Senate Republicans' campaign arm has dedicated a website to the controversy...