Boehner, R-Ohio, hinted darkly what would happen if the president acted outside the Constitution, the Hill newspaper reported.
"There are options that are available to us," Boehner said, and Republicans would discuss them at their annual retreat. The retreat begins Wednesday in Cambridge, Md.
House Republicans "will continue to look closely at whether the president is faithfully executing laws, as he took an oath to do," Boehner told reporters in Washington. "We're going to watch very closely, because there's a Constitution that we all take an oath to, including him, and following the Constitution is the basis for House Republicans."
Obama reportedly plans to announce in his speech he will unilaterally raise the minimum wage to $10.10 for employees under new federal contracts.
Boehner conceded the president probably had the authority to do that, but said it would have little impact.
"Let's understand something: This affects not one current contract," Boehner said. "It only affects future contracts with the federal government. So I think the question is, how many people, Mr. President, will this executive action actually help?"
The Hill said Boehner, citing his own career as a small-business owner, blasted Obama's call for a higher minimum wage, saying it would costs jobs and "hurt the very people the president purports to want to help."
Other Republicans said Obama needs to work with Congress if he wants to achieve results on job creation.
Democrats were more positive on Obama.
"Working with Congress, or if Congress wants, working without Congress, the president is going to get work done," Rep. Xavier Becerra, D-Calif., told reporters. Becerra is chairman of the House Democratic Caucus, and spoke after a party meeting in the Capitol, the Hill said. "We applaud him for that."