President Obama should be more mindful of the "mutual enemies" he shares with congressional Democrats before publicly criticizing them, the No. 3 House Democrat said Friday.

Rep. James Clyburn (D-S.C.), the outgoing House majority whip, chastised the president for criticizing "sanctimonious" Democrats on Capitol Hill who wish Obama had fought Republicans harder before agreeing to a deal to extend all expiring tax cuts for two years.

"Rush Limbaugh gives me just as hard a time as he gives Obama," Clyburn added. "So I'm on his side; we've got mutual enemies here," Clyburn told host Roland Martin in a radio appearance Friday morning.

Clyburn's remarks underscore the tensions between the White House and congressional Democrats after the latter group in the House on Friday voted to reject the tax deal Obama struck with the GOP this week.

Obama's waged a PR war this week in favor of his tax cuts, boldly predicting that Democrats would eventually come around to support the deal, largely as he's proposed.

"People will have the satisfaction of having a purist position and no victories for the American people. And we will be able to feel good about ourselves and sanctimonious about how pure our intentions are and how tough we are, and in the meantime the American people are still seeing themselves not able to get health insurance because of pre-existing condition, or not being able to pay their bills because their unemployment insurance ran out," Obama said Wednesday of recalcitrant Democrats.

Those words, Clyburn said Friday, were "much too tough."

"We're his friends. Look, I'm not Rush Limbaugh here. I want this man to succeed," he said.