Analysis by Chris Cillizza, CNN Editor-at-large

(CNN) -- NO COLLUSION, Donald Trump will tell you -- or, really, anyone -- if you ask about the ongoing special counsel investigation into Russia's interference in the 2016 election and the possibility that members of the Trump orbit colluded with the Russians to help him win.

And Trump is right! There is no definitive proof that he colluded with the Russians to throw the election his way. There's no smoking gun.

But, boy oh boy, is there a lot of smoke. So much smoke that it is choking the Trump administration's ability to do almost anything.

Consider what we learned Thursday morning when former Trump lawyer Michael Cohen pleaded guilty to lying to Congress about the nature and length of his interactions with Russians regarding the potential construction of a Trump Tower in Moscow.

Cohen had previously said that conversations about the possibility of a Trump-named development in Moscow ended in January 2016 -- coinciding with the beginning of the presidential primary season. On Thursday, Cohen admitted he had lied about that timing -- he had multiple conversations about the project until June 2016, briefed members of the Trump family about the progress of those conversations and even agreed to travel to Russia to discuss the project and raise the possibility of Trump doing the same.

Cohen said in court that he made those false statements in order to be consistent with Trump's political messaging and to be loyal to Trump.

That information runs directly counter to Trump's repeated assertions during the 2016 campaign -- and after he became president -- that he had no business dealings in Russia.

Here's Trump in July 2016, just one month after Cohen stopped talking about Trump Tower Moscow:

"I have nothing to with Russia, I have nothing to do with Russia. And even -- for anything. What do I have to do with Russia? You know the closest I came to Russia, I bought a house a number of years ago in Palm Beach, Florida. Palm Beach is a very expensive place. There was a man who went bankrupt, and I bought the house for $40 million and I sold it to a Russian for $100 million including brokerage commissions. So I sold it. So I bought it for 40, I told it for 100 to a Russian. That was a number of years ago."

And here is in October 2016:

"What do I know about the Russians? What do I know about the Russians? Then they said he borrows money from - I don't borrow money from the Russians. I promise you I've never made - I don't have any deals with Russia. I had Miss Universe there a couple of years ago other than that no. I had nothing to do."

And this from February 2017:

"And I can tell you, speaking for myself, I own nothing in Russia. I have no loans in Russia. I don't have any deals in Russia. President Putin called me up very nicely to congratulate me on the win of the election. He then, called me up extremely nicely to congratulate me on the inauguration, which was terrific. But so did many other leaders, almost all other leaders from almost all of the country. So that's the extent."

Now, even in light of Cohen's plea deal Thursday, Trump wasn't outright lying in any of those quotes. He didn't have active business dealings with Russia when he spoke in July 2016. But man, he is cutting it very, very close. If he's not outright lying, then he's not telling anything close to the full truth either.

Speaking of lying, that's what Trump accused Cohen of doing in his plea deal.

"He's a weak person," Trump said before taking off for the G20 summit in Argentina. "He was convicted with a fairly long-term sentence with things unrelated to the Trump Organization. What he's trying to do is get a reduced sentence." (Cohen previously pleaded guilty in the Southern District of New York to a series of crimes including willful breaking of campaign finance law.)

Could Cohen be lying? Sure! After all, he lied to Congress already!

But Cohen is the one who is risking his plea deal if it turns out he lied under oath to special counsel Robert Mueller and his team. Trump, by comparison, can say -- and tweet -- whatever he likes publicly without any criminal concerns. (The same is not true, of course, of the written answers to Mueller's questions that Trump and his legal team submitted last week.)

The smoke thrown off by the Cohen plea deal alone is substantial. But it only adds to all the other smoke that's already in the atmosphere surrounding Trump, his closest associates and Russians.

We know, for example, that Donald Trump Jr., Jared Kushner and Paul Manafort met with a lawyer linked to the Kremlin at Trump Tower in June 2016, lured to the meeting by a promise from the Russians that they had dirt on Hillary Clinton.

We know that Trump Jr. didn't initially tell the truth about the impetus for the meeting. We know that Donald Trump dictated Trump Jr.'s original misleading statement when the news of the meeting broke. We know that, despite the unanimous concision of the intelligence community that Russia interfered in the 2016 election to help Trump and hurt Clinton, the President has repeatedly expressed skepticism -- including with Russian President Vladimir Putin standing next to him -- of that fact. We know that former Trump national security adviser Michael Flynn pleaded guilty to lying to Mueller's team about the nature and extent of his contacts with Russian officials. We know that Trump, in the Oval Office, told then Russian ambassador Sergey Kislyak and Russia Foreign Minister Sergey Lavrov that he had "just fired the head of the FBI. He was crazy, a real nut job," and added: "I faced great pressure because of Russia. That's taken off." We know that Trump told NBC's Lester Holt that the real reason he had fired FBI Director James Comey was "this Russia thing."

I could go on -- and on -- but you get the idea. And if you don't get the idea then, well, you're trying not to get the idea.

Is it possible -- as Trump forever claims -- that all of this smoke is just smoke? That there is no actual fire? No proof of anything?

Sure. We don't have the Mueller report yet. And what we know publicly is smoke, not a full-on fire. But it is a whole hell of a lot of smoke. And it's making it very hard for the Trump administration to see anything at all.