On a host of issues, the list of requests is growing. Technology companies would like Mr. Obama to provide more visas for their workers, or at least more flexibility for them and their families as they await green cards for permanent residency. Consumer groups and organized labor want the Treasury Department to act on its own to limit financial incentives for companies that move overseas for tax breaks and stop so-called inversions. Democratic lawmakers are joining in as well, asking the president to act on his own on their pet issues.

“During your State of the Union address, you stated that you want to make 2014 a ‘year of action,’  ” Senator Dianne Feinstein, a California Democrat, wrote to Mr. Obama in March, in a letter requesting that he issue an executive order banning the import of assault or military weapons.

The go-it-alone approach has left the administration — which claims to be the most transparent in United States history — essentially making policy from the White House, replacing congressional hearings and floor debates with closed meetings for invited constituencies. ​

“The executive branch is not really set up to be a deliberative body like the Congress is,” said Andrew Rudalevige, a government professor at Bowdoin College who has studied the consequences of executive action. “The process is certainly stacked toward the policy preferences of the administration, and they’re going to listen to the people they think are right, which usually means the ones who agree with them.