Challenge: US Green Party Wins with Congress Majority

Can it be done? Can the US Green Party with Ralph Nader and all win a US election? Time would be early 2000s, i.e. the Gore vs Bush Election.
 
How many candidates did they run for Congress?
One reason Nader got as many votes was due to his reputation, as well as his position as being "none of the above". It would be harder to defeat people weren't as uncharismatic and as scandal-tarred as Bush and Gore.
 
I think any ATL that wants to raise a third party in the US would have to use a POD that tackles the two-party system.
 
Can it be done? Can the US Green Party with Ralph Nader and all win a US election? Time would be early 2000s, i.e. the Gore vs Bush Election.

It can be done only if the electoral college is scrapped in favor of a direct popular vote for POTUS -VPOTUS and if around the turn of the 19th-20th centuries the US takes a permanent, ongoing left turn politically and culturally.
 
More interesting and (barely) more possible: Green Party wins just enough Congressional seats to prevent either major party from having a majority, or enough Senate seats so no party gets the "magic 60".
 
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