Trump would need to achieve a result changing outcome in three of the following six states: NV, AZ, PA, MI, WI and GA. Some are more vulnerable to challenge than others by virtue of involving smaller margins of victory for Biden. (This assumes that no challenges of results for Trump are overturned or changed in favor of Biden. North Carolina is the only state where this possibility is plausible. But to the best of my knowledge, Biden has not brought any legal challenges to the vote counting process so far in any state.)
None of the lawsuits filed so far identify with specificity an alleged error supported by law and facts that is sufficient to overturn the current results. Most have already been dismissed. According to the Washington Post:
Bill Whalen, a political analyst at Stanford University’s conservative
Hoover Institution, compared a legal challenge based on what he has
seen and heard so far to the band-already-on-the-field kickoff return
that won the game for the University of California at Berkeley over
Stanford in 1982.
“It would be a once-in-a-lifetime coincidence of events — in other
words, Trump is going to lose,” Whalen said. “The president will run
out of legal options and the election will go to Joe Biden.” . . .
Kris Kobach, a former Kansas secretary of state who lost two statewide
races on the issue, said: “There’s very much a live legal controversy
in multiple states.”
He pointed to Pennsylvania, Georgia, Wisconsin and Nevada, where
Republicans have alleged that more than 3,000 voters who do not live
in the state cast their ballots there. . . .
Most of the Republican legal efforts have been small-scale and thrown
out by judges. In Nevada, a federal judge rejected Republicans’
request to intervene in ballot counting in Clark County, which
includes Las Vegas. Judges in Georgia and Michigan quickly dismissed
Trump campaign lawsuits last week. Supreme Court Justice Samuel A.
Alito Jr. ordered Pennsylvania counties to comply with state guidance
to keep late-arriving ballots separate, but did not direct officials
to stop counting ballots as Republicans requested.
It is hard to allege partisan bias in some of these states, such as Georgia, the closest state in the Presidential race, because in Georgia and some of the other states, the chief election administrator is a Republican elected official and all state election officials in this election have steadfastly assured the public that the vote counting in the Presidential election has been proper and proceeded as required by law.
The margins in all of these states except GA is in the tens of thousand of votes or more. Recounts almost never change an outcome that big. Recounts only change results about one time in ten and even then rarely do so with margins as large as seen in GA, let alone the other states. Recounts that prevail typically involve a few hundred to a few thousand vote margins.
There is also no reservoir of uncounted votes that has been identified that could flip most of these states (with the possible exceptions of GA and AZ although AZ would be a huge long shot). Unless there is some new discovery of tens of thousands of uncounted ballots from GOP leaning areas in storage lockers somewhere in several different states simultaneously, in the next several weeks, this isn't going to happen and there is no historical precedent for anything remotely similar to that happening in the last century plus.
Likewise, no credible challenge has been presented to any subset of votes cast sufficient to change the result in any of these states, just vague allegation of "fraud" in general which isn't enough to win a lawsuit. For example, the number of ballots received during an extended ballot receipt deadline are not large enough to change the outcomes in any of these states (with the possible exception of GA).
Also the clock is ticking on efforts to file lawsuits and fully litigate them. The Presidential electors vote on December 14, 2020 and any challenge to the certification of state results that would change the slate of electors chosen in a state would pretty much have to be decided by that morning. At the time this answer is written, this is about five weeks. If hypothetically, smoking gun evidence of computer hacking that changed results was discovered on December 15, 2020, for example, that would be too late.
Once the electors cast their votes in the state capitols on December 14, 2020, the outcome of the election become non-justiciable (i.e. beyond the jurisdiction of the courts). Congress could resolve a dispute if more than one slate of electors submits vote to Congress (which would have to happen in three of these states to change the outcome), but otherwise its job is ministerial and there is no good reason to think that the current Congress would not carry out that ministerial and public counting duty unfaithfully.
I would put the odds of a successful litigation challenge or other unconventional means of changing the outcome of the election that would be sufficient to upset the currently reported Biden election victory in the electoral college at 1-2% or less. This reflects the fact that three separate victories are required and that the outcomes of contests in different states, while not fully independent of each other, are also not strongly correlated to each other. There might be a 10-15% chance of one outcome changing victory, maybe a 5% chance of two, and a chance of 1-2% of three.
Acknowledgment of a Biden win from four of 53 sitting Republican Senators, George W. Bush, and some other notable current and past Republican officials also suggests that the Republican party elite does not have enough of a consensus to attempt an extreme end runs around the election result, even though most sitting Republican officials have declined to comment on whether or not Biden has won the Presidential election yet. The fact that Fox News, the leading conservative media outlet in the U.S., as well as most other major media outlets in the United States have called the election for Biden, also reduces the likelihood that conservative judges and politicians will feel that there is a basis to support Trump's legal challenges strongly with extraordinary measures like mass protests and unprecedented legislative action at the state level (which would probably be illegal as ex post facto legislation in any case at this point).
There has also never been a coup in the United States and the indications from the military (not just the Secretary of Defense fired today) is that a coup will not happen this time either.