Donald Trump introduced his concept of “principled realism” at the United Nations this morning. Mike Pence has spent the last couple of weeks introducing a similar approach at the White House and on Capitol Hill. CNN’s Manu Raju reports that the vice president has busied himself with diplomatic missions between the two ends of Pennsylvania Avenue to restore relations between Trump and Senate Republicans. The efforts appear to be paying off just when closer relations will be needed most:

The private outreach is part of a more concerted White House effort to repair relations Trump damaged with his own party over a tumultuous August, following the failure of the GOP effort to repeal Obamacare and a slew of White House controversies, including the President’s controversial handling of a deadly protest in Charlottesville.

And it now comes at a critical time: The White House is desperately trying to revive its health care push before a September 30 deadline — and needs senators like Murkowski to salvage the President’s agenda. But of course, it hasn’t always been smooth — especially as Trump has tried to circumvent Republicans and cut deals with Democratic leaders — over the GOP leadership’s objections. …

Behind the scenes, Vice President Mike Pence has played a key outreach role, leaning on his longstanding relationships with senators — even those who are frequent targets of Trump’s derision — to help underscore the point that they’re all on the same team. He often praises senators for the job they’re doing and says the President feels the same way, according to several senators who have spoken with the vice president.

Raju notes that Lisa Murkowski got direct contact with Trump as a way to get past their public squabble, about which Murkowski seemed gracious and appreciative. Mitch McConnell had a private meeting with Trump two weeks ago after getting repeatedly blasted by the president, which seemed to tamp down the feud if not exactly resolving it. Trump has begun to campaign for McConnell’s favorite in the Alabama special election, Luther Strange, rather than populist favorite Roy Moore, a sign of rapprochement with the Senate Majority Leader.

Everyone else has gotten the Pence treatment, Raju reports — including Bob Corker, John McCain, Jeff Flake, and McConnell as well. It reads a little like a good cop/bad cop routine, where Trump has flashes of temper and Pence then intercedes to restore intraparty comity and cooperation. The biggest challenge for Pence in this effort is Trump’s short-term “transactional” approach to relationships, Raju writes, a quality to which the Republican caucuses on Capitol Hill are grudgingly getting accustomed. John Cornyn told Raju that they’d have to get used to mercurial approach: “What choice do I have?”

Not much, especially if Republicans want to cut deals with the White House ahead of Democratic leadership. The Graham-Cassidy bill will test Pence’s diplomatic acumen. Trump has made it crystal clear that he’ll sign anything that can be spun as an ObamaCare repeal, and the chair of the House Freedom Caucus threw them a bone yesterday. Rep. Mark Meadows said the House would pass Graham-Cassidy in its current form, as long as it didn’t give too much away to Susan Collins and other moderates. If the CBO can deliver a reconciliation-enabling score soon enough to get votes on the floor of the Senate and House, Pence could pull off quite a coup for Trump … assuming he doesn’t complicate Pence’s work any more than he has.