WASHINGTON — Welcome to Barack Obama’s split-screen presidency.

On one side: a confident Obama making campaign-style stops around the country and ridiculing his political opponents to the delight of cheering supporters. On the other side: an increasingly unpopular president hobbled by gridlock on Capitol Hill and a steady stream of vexing foreign policy crises.

Obama has long sought refuge outside of Washington when his frustrations with the nation’s capital reach a boiling point. But his ability to rally public support in a way that results in progress for his legislative agenda has perhaps never been weaker than it is as he nears the midpoint of his second term.

To the White House, the take-away is that Washington — and the Republican Party in particular — is out of touch with the American people and failing to address their priorities. But to GOP leaders, Obama’s activities in a midterm election year reinforce their view of a president more focused on soaring speeches and partisan politics than on working toward compromise solutions to the nation’s problems.

Each side has at least some evidence to support their case.