The Kentucky senator also said it was "extremely irritating" that Congress has a reputation as do-nothing.
Photo Senate Majority Leader Mitch McConnell during a news conference at the Capitol last month.
Picking fights with the Senate GOP leader - after Trump's on-again-off-again relationship with House Speaker Paul D. Ryan (R-Wis.) - show how hard it will be for Republicans to reach the goals on their agenda heading into the fall.
Trump's jabs at McConnell on Wednesday following the Kentucky Senator's earlier defamatory statement emphasizing the President's inexperience and ignorance of how the Senate works and thus called Trump's expectation of the Obamacare repeal as being excessive.
"If he doesn't get that done, then you should ask me that question", he said.
"That I can tell you, it shouldn't have happened". After all, McConnell has a narrow majority to deal with.
"All I hear is repeal and replace".
But Trump couldn't care less about McConnell's stand.
That drew a tweet Wednesday from Dan Scavino Jr., the White House social media director.
On his McConnell criticism: "I said, Mitch, get to work and let's get it done". But Mr Trump has continued to tweet about the issue, and wrote that "unless the Republican Senators are total quitters, Repeal & Replace is not dead!"
The early morning tweet is a continuation of the president's singling out of the one man tasked with leading the GOP in the Senate. "They look like fools and are just wasting time", he tweeted on July 29. He and his Senate Republicans have been utterly uninterested in examining Trump's conflicts of interest and potential violations of the emoluments clause. They are laughing at R's. "We should not make the mistakes of the past". But the beginnings of the broader argument against the GOP are all right there, in 140 characters at a time. The Senate GOP has increasingly shrugged off suggestions from Trump as he faces low approval ratings and struggles to enact his agenda. That's because all of them had political careers long before Trump became a serious force within the party. The White House has said it hopes for votes on tax legislation in both chambers by November. The attacks are a risky approach considering Trump's slumping job approval ratings among his most fervent supporters.
Second, in a week in which much of the country is disturbed that the president lacks the gravitas, discipline and judgment to be commander in chief, Trump's attack reinforces the idea that he is motivated by personal pique and is incapable of dispassionate strategizing.