President Obama’s repeated use of presidential powers is causing a tough problem — his own supporters now expect him to use it to achieve everything they want.

From immigration to the minimum wage, congressional Democrats and liberal activists this week urged Mr. Obama to declare an end run around Capitol Hill, assert executive authority and make as much progress as he can on the expansive agenda he laid out for his second term.

A day after Mr. Obama denounced income inequality, progressive lawmakers said he should take the lead by issuing an executive order requiring all federal contractors to pay workers more than the minimum wage. A dozen lawmakers and immigration activists held a news conference outside the Capitol on Thursday asking him to halt all deportations as a down payment on an eventual immigration bill.

“To not use his executive authority is not just unstrategic; it is cruel,” said Tania Unzueta, a strategist with the National Day Laborer Organizing Network.

On immigration, Mr. Obama raised expectations when, after years of denying he had such powers, he issued a policy last year saying he no longer would deport young illegal immigrants, the “Dreamers” who were brought to the U.S. as minors by their parents and are considered the most sympathetic cases. He said he was using prosecutorial discretion.

More than two dozen House Democrats have written a letter to Mr. Obama saying he can expand that authority to encompass nearly all 11 million illegal immigrants.