Washington (CNN) For months, President Donald Trump has relentlessly attacked the Russia probe, and his missive Wednesday saying Attorney General Jeff Sessions should stop the investigation reignited the question of whether Trump's actions would constitute obstruction of justice.

Soon after becoming President, Trump asked then-FBI Director James Comey to stop investigating former national security adviser Michael Flynn, according to Comey. Trump later fired Comey, and said Russia had been on his mind when he made the decision. After special counsel Robert Mueller was appointed to investigate Russian interference in the 2016 US election, Trump apparently considered firing Mueller.

Now as Mueller's first trial is underway, of the President's former campaign chairman Paul Manafort, Trump has ramped up calls to end the whole probe. "This is a terrible situation and Attorney General Jeff Sessions should stop this Rigged Witch Hunt right now, before it continues to stain our country any further," Trump tweeted.

As Mueller has been investigating Russian interference and any links between the Russian government and the Trump campaign, his team is also exploring whether Trump has attempted to obstruct the investigation.

Yet prosecutors say obstruction is not a clear-cut matter and corrupt "intent" would have to be proved. And ultimately, Trump's actions might not be tested in a court of law but rather in the chambers of Congress. The traditional venue for action against presidential wrongdoing is the impeachment process, where it would fall to the House and Senate to determine whether Trump's actions warrant punishment.

Trump's tweets prompted an immediate response from Rep. Adam Schiff of California, the top Democrat on the House Intelligence Committee, who said on Twitter that the demand from the President "is an attempt to obstruct justice hiding in plain sight" and added, "America must never accept it."

Sessions last year recused himself from the investigation related to Trump's 2016 presidential campaign. (Sessions had earlier failed to disclose during his Senate confirmation hearing contacts with Russia's ambassador to Washington.) Deputy Attorney General Rod Rosenstein appointed Mueller as special counsel to look into the Russian interference and any Trump campaign officials' involvement.

Trump has repeatedly denied any connections and has also said there has not been any obstruction. As Manafort's trial began this week, the President repeated his "there was no collusion" mantra. Earlier this week Trump's lawyer Rudy Giuliani said on CNN that Trump would not be found "colluding" with the Russians.

Yet as much as the word "collusion" has been invoked to describe possible complicity between Trump associates and Russian operatives, there is no federal crime of "collusion" in this kind of investigation.

The crimes that might be charged would be conspiracy, making false statements, destruction of evidence or obstruction of justice.

That last offense covers any attempt by someone to "influence, obstruct, or impede" the "due administration of justice." The key question in a criminal case is whether the individual acted with a corrupt intent.

Former federal prosecutor and CNN legal analyst Renato Mariotti suggested that special counsel investigators may view Trump's directive to Sessions as evidence of such corrupt intent.

"They think this is more evidence of corrupt intent. I think that the Mueller team is adding more tabs to their exhibit binder," Mariotti told CNN's Kate Bolduan on "At This Hour" in response to a question about what Mueller's team might think about the latest tweets. He added that "what these tweets are are presidential statements."

Mariotti cautioned that he did not think the tweet would be used by Mueller as the specific basis for an "obstructive act," but said that "today's tweet is a very, very strong indicator that the President is willing to do whatever it takes to make sure that he and his friends are protected from the investigation."

Giuliani attempted to downplay the President's tweet on Wednesday by saying it was not a presidential order.

"The President was expressing his opinion on his favored medium for asserting his First Amendment right of free speech," Giuliani told CNN's Dana Bash. "He said 'should', not 'must', and no presidential order was issued or will be."

White House press secretary Sarah Sanders echoed that interpretation, telling reporters that Trump "wants to see it come to an end, as he has stated many times, and we look forward to that happening." She added, "The President is not obstructing. He's fighting back."

Congress' job?

As legal analysts have noted, Trump's efforts to stop the Russia probe would be more likely tested in Congress than in the courts.

Department of Justice opinions dating to the 1970s and the Watergate era conclude that a president cannot be indicted. (The Supreme Court has never ruled on the question.) So, traditionally, the avenue for charges against a President is the impeachment process, as happened with Richard Nixon in the 1970s and Bill Clinton in the 1990s.

Impeachment is political and comes down to votes: a majority in the US House of Representatives to impeach and a two-thirds vote of the US Senate to convict. Clinton was impeached by the House, but the Senate failed to convict in 1999 and he served out his full second term. Nixon resigned in 1974 as impeachment charges related to the Watergate cover-up loomed; the matter never got to the full House.

Both the Nixon and Clinton ordeals began with reports from special prosecutors in roles akin to Mueller's, and both covered obstruction of justice, along with other charges.

Currently, both the House and Senate are controlled by Republicans.

Whatever action awaits Trump, if any, the President is already on the defensive. On Wednesday, he said on Twitter that Manafort had worked for him only "for a very short time" and the charges against his former campaign manager "have nothing to do with Collusion," which he referred to as "a Hoax!"