Trump spokeswoman Sarah Huckabee Sanders confirmed to reporters Thursday in Bridgewater, New Jersey, near the president’s golf resort, that Trump and McConnell spoke by phone on Wednesday before Trump sent the first tweet. "Health care was obviously discussed," she said without giving further details.

Related: Sanders Institute delivers Medicare-for-All research paper to Congress

The public spat has some Republicans calling for calm as Congress is poised to take on an array of tough issues next month, including the debt ceiling, appropriations and taxes. Representative Tom Cole of Oklahoma said on CNN that he didn’t want to take sides and that McConnell and Trump need each other to press on with the party’s agenda. Cole said not repealing Obamacare was a congressional failure, not a presidential one. However, he said, “This isn’t a time we need to throw rocks at one another.”

Former House Speaker Newt Gingrich, a Republican, on Thursday defended McConnell on Fox News. “The president can’t disassociate himself with this,” Gingrich said of the health-care vote. “It was a collective failure.”

Gingrich said it was “goofy” for Republicans to be turning against one another, and that given the complexity of the issue he believes it could take between three and five years and as many as a dozen legislative attempts to replace the Affordable Care Act. Gingrich said he also is concerned that if Republicans bungle attempts to overhaul taxes after the August recess, it could be a political “disaster.”

The back-and-forth between the president and the Senate Republican leader highlights the starkly different governing styles of the two men. The president’s freewheeling and off-the-cuff actions contrast with McConnell’s rigorously disciplined method of leading the Senate. Though McConnell has largely refrained from criticizing Trump, he has on occasion critiqued the president’s use of Twitter as unhelpful to GOP lawmakers’ efforts to stay on message in pursuing their priorities.

McConnell’s remark also prompted a rebuke Wednesday from Dan Scavino, the White House social media director. “More excuses,” Scavino wrote on Twitter. “@SenateMajLdr must have needed another 4 years - in addition to the 7 years-- to repeal and replace Obamacare.....”

McConnell spokesman David Popp said in an email that the majority leader has already spoken about the path forward on Obamacare repeal and had no further comment.

The clash follows weeks of mismatched strategy and building tension between Trump and McConnell before the collapse late last month of the GOP’s drive to replace Obamacare.

Shortly before a week-long July 4 recess, Trump tweeted that Republicans should simply repeal the Affordable Care Act rather than replace it -- just as McConnell was seeking to reel in wayward conservatives to a broad rewrite of the health law. Later, as McConnell’s GOP-only rewrite was losing support, Trump invited Republican senators to the White House and urged them to continue. Finally, McConnell brought a bare-bones repeal to the Senate floor and it failed by one vote.