Ryan described the charm offensive as "helpful" during an interview on Greta Van Susteren's "On the Record" on Thursday, adding: "The question is, is it real and will it last? If it is real and if it does last, then I think we've got a chance of getting a down payment on the problem fixed."
For the most part, these conversations are taking place outside congressional leadership circles.
Cole told The Washington Post earlier this month that he hadn't been contacted in months by the White House legislative affairs office. Staffers quickly reached out to schedule an appointment between Cole and the White House's new legislative director, Miguel Rodriguez.
"They've been trying," Cole said, saying members appreciated that Obama spent an hour and a half speaking to the House GOP Conference of March 13 and shook hands and took photos with any member who came up to him afterward. "He was not whisked out. That was not lost on anybody."
House Administration Committee Chairman Candice Miller, R-Mich., who has clashed with the administration over canceled White House tours and other issues, recently huddled in her office with Rodriguez on how to promote natural-gas-powered vehicles.
"If you're looking for a Republican to work with you on that, you've found one," she recalled telling Rodriguez.
Miller struck a similarly positive tone when she got a chance to ask the president a question during his recent closed session with House Republicans, who face regular attacks from the Democratic Congressional Campaign Committee.
"Please don't be a stranger," Miller remembered telling Obama. "And please don't believe anything the DCCC puts out on the House Republicans."