Earlier on Friday, Macon Phillips, the White House director of digital strategy, tweeted that "#compromise" was the hashtag of the day for tweets of this nature.
The campaign is also crowdsourcing, asking followers to tweet them additional handles of GOP lawmakers.
But could this strategy have an unintended consequence for the president? With 9.4 million followers, Obama's campaign account is one of the most followed. Mentioning GOP foes to Obama's followers could help boost their followings on Twitter.
By midafternoon on Friday, that seemed to be the case.
"Thanks @BarackObama for pushing @RoyBlunt over 11,000 followers today!" tweeted Amber Marchand, communications director for Sen. Roy Blunt, R-Mo.
"Looking forward to all the new followers @BarackObama sends my way today in his Twitter spam campaign," tweeted Rep. Patrick McHenry, R-N.C.
Katie Hogan, a spokeswoman for the Obama campaign, declined to comment, but a House Republican staffer thought Obama was making a mistake.
"He’s going to be jumping into a dogfight, given that 80 percent of our conference, and 90 percent of the freshmen are on Twitter," said the staffer, who is not authorized to talk to the media. "Does he really want to go there?"