(CNN) President Donald Trump resumed his public feud with Senate Majority Leader Mitch McConnell Thursday over his party's failure to repeal and replace the Affordable Care Act, a sign of the fraught relationship between two branches of government that are both controlled by Republicans.

"Mitch, get back to work and put Repeal & Replace, Tax Reform & Cuts and a great Infrastructure Bill on my desk for signing. You can do it!" Trump tweeted , his third tweet in two days calling out the Senate majority leader.

"Can you believe that Mitch McConnell, who has screamed Repeal & Replace for 7 years, couldn't get it done. Must Repeal & Replace ObamaCare!" the President tweeted earlier.

Trump commented Thursday about his ongoing spat with McConnell, telling reporters that if McConnell can't convince Republican senators to repeal and replace Obamacare, then it's time to consider stepping aside. Asked whether McConnell should resign, Trump said to wait and see if he can get repeal and replace done. "Then ask me," he said.

The public comments continue a public exchange of criticism between the GOP leaders of the Congress and White House this week, both of whom have an ambitious policy agendas that have struggled to make progress. On Tuesday, McConnell said Trump had " excessive expectations " for the legislative process and suggested there was a false perception that Congress is underperforming in part "because of too many artificial deadlines unrelated to the reality of the legislature, which may have not been understood."

Trump responded to that criticism Wednesday, tweeting: "Senator Mitch McConnell said I had 'excessive expectations,' but I don't think so. After 7 years of hearing Repeal & Replace, why not done?"

Senator Mitch McConnell said I had "excessive expectations," but I don't think so. After 7 years of hearing Repeal & Replace, why not done? — Donald J. Trump (@realDonaldTrump) August 9, 2017

A White House official told CNN Trump and McConnell spoke on the phone Wednesday about the path forward on health care and did not dispute that it was an animated conversation. A source familiar with the call said the conversation occurred while Trump was on his New Jersey golf course.

Asked about that conversation, Don Stewart, a spokesman for McConnell, responded, "I don't have any readouts of his calls." In response to Trump's tweet, he provided the same statement released by McConnell's office in response to Trump's Wednesday comments: "The leader has spoken repeatedly about the path forward regarding Obamacare repeal on the Senate floor, at media availabilities multiple times and in Kentucky."

Asked about Trump's relationship with McConnell and how they would characterize their call, White House press secretary Sarah Huckabee Sanders said, "I think you can see the President's tweets. Obviously, there is some frustration."

Dan Scavino, the White House director of social media and a close aide to Trump, also weighed in earlier Wednesday -- before Trump's tweets -- against the Senate majority leader. Scavino, who has ardently defended the President against critics in the past, posted McConnell's exact remarks on his personal Twitter and added his own take.

"More excuses. @SenateMajLdr must have needed another 4 years - in addition to the 7 years -- to repeal and replace Obamacare," Scavino wrote

More excuses. @SenateMajLdr must have needed another 4 years - in addition to the 7 years -- to repeal and replace Obamacare..... https://t.co/6FOVBm6BQU — Dan Scavino Jr. (@DanScavino) August 9, 2017

Scavino's tweet echoed Twitter attacks that Trump himself has made against congressional Republicans. Late last month, the weekend after the Senate failed to pass a bill to repeal and replace the Affordable Care Act, Trump made a series of tweets attacking Republicans and urging them to change Senate rules to allow more bills to pass with a 51-vote majority, rather than 60.

"Republicans in the Senate will NEVER win if they don't go to a 51 vote majority NOW. They look like fools and are just wasting time," he wrote in one tweet

Republicans in the Senate will NEVER win if they don't go to a 51 vote majority NOW. They look like fools and are just wasting time...... — Donald J. Trump (@realDonaldTrump) July 29, 2017

However, Republicans were already operating under "budget reconciliation," which would have allowed them to pass health care legislation with a 51-vote majority. And since Republicans have a 52-48 majority in the Senate, they could have passed it if the party was united, but three Republicans defected and the bill failed to advance.

Reconciliation can only be used once each fiscal year, and if Republicans want to use it again on upcoming legislative efforts like tax reform, they must first pass a budget for the fiscal year 2018.

JUST WATCHED Trump, McConnell spar over expectations Replay More Videos ... MUST WATCH Trump, McConnell spar over expectations 06:23

Asked about the Trump-McConnell feud on CNN's "New Day" Thursday, Sen. Ron Johnson, R-Wisconsin, acknowledged, "We should have gotten this done. The ball was in our court."

"I'll let this President speak for himself and his tactics," he later said. "The fact of the matter is we need to come up with the policies to reduce premiums. That's what we'll be talking about. We need to be honest in terms of what the root cause analysis is. That's in the lap of Congress, in the lap of the House and the Senate. Obviously, we need as much help and support from the administration as well as we're doing this."

Republican Sen. Rob Portman, who was asked about McConnell's comments on Fox News Wednesday morning, also disagreed that the President had "excessive expectations" and made the case that Democrats were to blame.

"I think the President's expectations was that we would work together to get these things done and frankly we haven't had a lot of buy-in from the Democrats on this stuff, and that's too bad," he said.