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Earlier this month, Mr. Obama decided to delay by one year, to 2015, the employer mandate requiring firms of 50 or more full-time workers to provide health coverage or pay fines.

Mr. Cruz said if Obamacare were a good thing, the president would want the mandate to kick in before the 2014 midterm elections.

Republicans and some Democrats have derided the employer mandate as a job-killing measure that’s prompting fast-food chains and other franchises to reduce payroll to stay under the 50-employer cap. The mandate defines a full-time work week as 30 hours, and some employers have reportedly cut workers’ hours to make sure they are considered part-time.

The White House pushed back against those claims on Tuesday in a blog post and graphics that show promising job growth within the restaurant industry over the last three years.

“Recent news stories have cited anecdotes that restaurants are cutting employees’ hours and refraining from hiring workers due to the ACA,” wrote David Vandivier, chief of staff for the Council of Economic Advisers. “In reality, however, restaurants have had the fastest job growth of any industry in the retail and food services sector since the Affordable Care Act was signed into law.”