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Rep. James P. McGovern, Massachusetts Democrat, said if Republicans really wanted to defend Congress‘ rights and prerogatives, they would have written the bill differently. As it is, he said, it’s a political document.

“You guys just don’t like the president. I get it. But get over it,” he said. He said the bill is “likely unconstitutional” and would result in scores of lawsuits.

Simon Lazarus, senior counsel at the Constitutional Accountability Center, said what Mr. Obama has done in carrying out the laws is no different from what President George W. Bush or his predecessors did, though Mr. Obama is doing it often.

He said with complex laws, the president must have the ability to delay implementation of pieces in order to ensure the overall law is carried out.

“It’s not illegal and it’s certainly not a violation of his constitutional duty,” Mr. Lazarus said. “It’s actually exactly what the Constitution contemplates.”

Mr. Lazarus said Congress already has ways to overcome what they see as presidential obstruction — either by enacting laws or winning elections.

“This legislation is a recipe for moving the forum, the political theater, to another venue, namely the courts, and that is not what the Constitution created the courts to do,” he said.

Immigration rights activists viewed the House move as an effort by Republicans to try to roll back Mr. Obama’s 2012 order that gave tentative legal status to a subset of illegal immigrants called “dreamers.”

“It seems House Republicans want us all to know that they not only hate the president, they hate immigrants, too,” said Frank Sharry, executive director of America’s Voice.