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“As he has so many times in the past, Mr. Romney seems to forget he’s a Republican,” said Perry spokesman Ray Sullivan. “Mr. Romney has been running for president full time for nearly five years and has failed to issue a specific plan on Social Security. Rick Perry and other conservatives are courageous enough to be honest about federal spending and entitlements, whether Mr. Romney and the liberals like it or not.”

In an appearance on Fox News Channel on Wednesday, Mr. Perry personally repeated the line of attack.

“We need to nominate someone who has a stark, clear difference between the Republican nominee and President Obama,” he said. “We don’t need to nominate Obama-Lite.”

The two Republicans also traded blows on each other’s records on jobs, with the Romney camp contending the unemployment rate in Texas has doubled on Mr. Perry’s watch and the Perry camp pointing out that Massachusetts ranked 47th in job creation during Mr. Romney’s administration.