The approach, which is being implemented in part by a well-organized group led by former aides to President Obama, involves targeting vulnerable GOP Senate incumbents for defeat by portraying them as unwilling to fulfill the basic duties of their office. The idea is to so threaten the Republicans’ Senate majority that party leaders will reconsider blocking hearings on Garland’s nomination.

“You’re going to be surprised at how hard we’re going to work to make sure this is on the front pages of all the papers,” Senate Minority Leader Harry M. Reid (D-Nev.) told reporters after meeting with Garland on Thursday.

At the White House, Obama held a conference call with thousands of supporters across the country while senior adviser Valerie Jarrett met on Capitol Hill with members of the Congressional Black Caucus. White House press secretary Josh Earnest told reporters he had no details of a specific request Obama was making on the call. “But I think the president sent a pretty clear signal, though, that this a high priority of his, and he hoped that this would be a priority that people all across the country would share,” he said.