You got your timeline mixed up.
May 15: Democrats pass Cares Act II that includes $1,200 direct payments
May 15th - September 15th: Mitch McConnell never brings The Cares Act II to The Senate floor for a vote so that it can pass and we can receive the second $1,200 check.
September 15th - December 21st: Republicans propose $600 payments instead of $1,200 payments and they also attach some bullshit to the Bill that would benefit Trump after he leaves office. This stuff was added by Steve Munichin on behalf of Trump. It was a money grab for Trump. Democrats say hell no that's bullshit and an insult to all of the people who have been waiting months for help. Then people attack Pelosi for not accepting the $600 deal that is half of what Democrats proposed and includes all of that extra Trump bullshit.
December 21st: Trump goes against Republicans and calls for $2,000 checks in an effort to try and save the two Georgia Senate seats that were in a runoff that was being held on January 5th. Democrats say sure make them $2,000 and the rewrite the Legislation to make the checks $2,000 and hold a pro Forma vote that passes in The House and they sent it to The Senate.
So now on December 22nd Trump, Democrats, and The People all want the $2,000 checks but Mitch McConnell immediately shoots them down. So then Ossof and Warnock started to include the $2,000 checks in their campaign by saying that if Democrats win the Senate you will receive $2,000 checks which was and is still true.
December 29th: While Trump and the Democrats are asking Mitch McConnell to approve the addendum to make the checks $2,000 instead of $600 Mitch McConnell decides to go nuclear and just approve the $600 checks. Democrats then said that once they win The Senate which they did that they would ensure that people receive the full $2,000.
The whole semantics of $600 vs $1,400 vs $2,000 really comes down to when and how you receive your check. Payments started going out on December 30th.
If you already got your $600 you will receive an additional $1,400. That is your $2,000 check it just came in two separate checks.
If you still have not received your $600 then you will get a single check for $2,000.
It was never stated that there would be a $2,000 check on top of a $600 check.
The only reason why people are confused is because the Pro Forma vote in the Senate was approved for the $600 checks while Democrats and Trump were still asking for Mitch McConnell to approve the $2,000 addendum.