(CNN) Donald Trump, we know, is like a dog on a bone. Once he gets his teeth into something, he doesn't usually give up until it's dead or maimed, politically speaking of course.

The latest victim of Trump's sharp teeth is Senate Majority Leader Mitch McConnell, who Trump suggested on Thursday might consider stepping down from his post if he can't get health care reform, tax reform and infrastructure spending through Congress.

"You can ask the question" of McConnell stepping down, Trump told the pool reporters gathered at his golf club in Bedminster, New Jersey during his 17-day long working vacation.

It's Trump's latest -- and most aggressive -- attempt to troll McConnell over the last 24 hours.

In a trio of tweets, Trump slammed McConnell as an ineffective leader. On Wednesday afternoon, Trump tweeted : "Senator Mitch McConnell said I had 'excessive expectations,' but I don't think so. After 7 years of hearing Repeal & Replace, why not done?" Then, this morning, he tweeted a variation on that theme : "Can you believe that Mitch McConnell, who has screamed Repeal & Replace for 7 years, couldn't get it done. Must Repeal & Replace ObamaCare!" And then, again, in the early afternoon : "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!"

It's easy -- amid Trump's continued incendiary comments about North Korea and his broader penchant for just, well, saying things -- to gloss over this. We shouldn't.

Consider this: Trump is leaving open the possibility that the Senate majority leader -- of his own party! -- should step down if he can't get done what Trump wants done. That is not normal politics. If anything close to this happened with President Barack Obama and then-Senate Majority Leader Harry Reid, it would have been the lead story of every newscast in the country. It would have launched a thousand articles delving into the collapse of their relationship -- and what it all meant for the party and its chances of getting something done.

What's more: The strategy behind this latest series of attacks is difficult (impossible?) to ascertain.

Sure, Trump's base will like it -- McConnell is the face of a party establishment they loathe and think is deeply ineffective. But Trump's base is going to be with him no matter what he does or who he attacks. It's not as though they are going to be more for him because he is attacking McConnell.

Given that, there's no obvious upside for Trump. And there's a very clear downside: That he loses the trust, respect and collegiality of everyone from McConnell to the rank-and-file Senate Republicans who owe their elections (or reelections) to McConnell.

"@SenateMajLdr has been the best leader we've had in my time in the Senate, through very tough challenges,'" tweeted Utah Sen. Orrin Hatch in the moments after Trump's latest attack. "I fully support him." There will be more tweets and statement like this from GOP senators.

This looks like a classic case of cutting off your nose to spite your face by Trump. To get anything -- literally, anything -- done in the coming months or years, he needs McConnell. And, McConnell a) isn't going anywhere and b) has no serious threat to his leadership position.

What Trump is doing is akin to visiting a friend's house, saying it's a dump and then asking if you can stay there for a few weeks while your own house is being renovated.

If McConnelll ever had an inclination to help Trump for the good of the party, it's hard to see how the past 24 hours don't wipe that away entirely.

The way the Senate -- and every other legislative body -- works is trust and goodwill. The attacks on McConnell -- coming after Trump's repeated attacks on Sen. John McCain, his calling out of Alaska Sen. Lisa Murkowski on health care, his threat to Nevada Sen. Dean Heller on his vote and his repeated attacks on former senator and now Attorney General Jeff Sessions -- effectively zero out Trump's already dwindling supply of either trust or goodwill among the 52 Republican senators.

Trump may not care -- which is his right. But this is a fight he can't win -- and shouldn't keep stoking. Which, of course, means he almost certainly will.