Trump participated in a discussion with retired Army Lieutenant General Michael Flynn.
McConnell is said to be telling colleagues that he doesn't expect Trump to finish out the term as president.
Senate Majority Leader Mitch McConnell promises there is "zero chance" Congress won't raise the nation's debt ceiling with a deadline fast approaching.
In a phone call on August 9, Trump blamed McConnell for the Senate's troubled efforts to repeal and replace the Affordable Care Act.
White House press secretary Sarah Huckabee Sanders released a similar statement Wednesday evening.
Mr. Trump also has been prodding Capitol Hill lawmakers, and Mr. McConnell in particular, to get his stalled legislative agenda moving. He's facing a primary challenger whom Trump seems to favor.
Trump and McConnell did not provide comment to the Times for its article.
On Tuesday night at a raucous rally in Arizona, the president threatened a government shutdown if Congress does not provide funding for his signature campaign promise, a wall along the U.S. -Mexico border.
However, McConnell has privately fumed about Trump's attacks on Republicans like the three senators who voted against the Obamacare repeal bill, as well as Sens.
When Congress returns in September, McConnell said that the key objective was putting together a comprehensive tax reform plan.
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