Trump can take to the streets and declare himself president for the next term because the election results were not validated.
He can challenge the 'never used' legal procedures in court and of course have his lawyers lie about it in public.
They could fire up enough people and get enough momentum so that a few Republicans could be pressured to not vote to validate the election results.
If he refused to physically leave the White House - who would make him leave? Imagine if he invited his supporters to 'come to Washington to Defend the President' and they set up camp by the thousands around the WH. And they'd be armed. Is the National Guard going to start shooting? The longer Trump stays there, the more entrenched his legitimacy.
Especially if there is violence, it'd really flare tensions.
If people believe that the election was stolen, they'd also be hard pressed to be told what the actual, legal procedures are for dealing with a failed vote validation, and so it would be a matter of populism as much as legality.
That's how coups happen: enough political, populist, physical force to carry the momentum beyond established legal norms.
[1] https://www.hup.harvard.edu/catalog.php?isbn=9780674737266
Mussolini's coup, 'March On Rome' [1] is a good reference, but there are plenty of historical examples.
Needless to say, the conditions on Jan 6. parallel key elements many historical coups.
" The highest-ranking U.S. officer, Chairman of the Joint Chiefs of Staff Gen. Mark Milley, and other top military leaders made informal plans to stop a coup by former President Donald Trump and his allies in the run-up to the 2020 presidential election," [2]
(there are many sources for this).
So first, you're at odds with the Chairman of the Joint Chiefs of Staff, who likely has an inkling of what was a 'coup' is.
Fabricating a constitutional crisis and fomenting mass populist furor is definitely a path to a coup, which he was obviously pursuing.
The reason that the VP et. al. reconvened immediately after the Jan 6 riots, directly in the 'still dangerous' aftermath - was because they wanted to make sure that the proceedings were as legitimate as possible, with little deviation from historic and traditional norms thereby minimizing the ability of the former President to create false narrative about it, and reducing his ability to sneak procedural and legal barbs into the process, which is defined by some really vague old laws and is established by tradition and precedent as much as anything.
Here are some good historical references, they make for good comparisons [3][4].
I think the chances of him fully taking over were small, but the chances of him mangling up processes and creating a kind of an oddball legal situation which would take many months to resolve while his supporters increased their level of agitation (we saw millions in the streets for BLM, no reason to believe his supporters mightn't have done the same) as a very real possibility.
[1] https://en.wikipedia.org/wiki/March_on_Rome
[2] https://www.usatoday.com/story/news/politics/2021/07/15/join...
[3] https://en.wikipedia.org/wiki/List_of_coups_and_coup_attempt...
[4] https://en.wikipedia.org/wiki/List_of_coups_and_coup_attempt...