Yes, they do. But you have not established that he lied. You’ve just assumed he was lying. We do that with Trump because he lies so often that it’s a safe assumption. To do so with Biden implies he’s at that same level.
As I pointed out, your issue seems to be that you are using the same definition of “unity” that Republicans are disingenuously using to attack Biden–as it wasn’t the definition they used when Trump called for unity. Biden hasn’t attacked any Republican since being in office. He’s actively attempting pushing through his COVID-relief bill without using reconciliation–which requires him to reach out to at least 10 Republican Senators. He met with a bipartisan committee that was concerned about the $1400 stimulus going to people who didn’t need it, as well as the high bill, and worked with them to try and handle the issue.
Granted, this is not likely something you knew about. But you just assumed that he was lying, without even giving him a chance. You ignored that he has a history of trying to work in a bipartisan way, and has Republican friends.
“Politicians lie” is not proof that Biden was lying in that one particular situation. It very much seems like he’s going to try for unity. Sure, I expect that Republicans will at some point become obstructionists again, and he will have to abandon that tactic. But, for now, he seems entirely willing.
Trying to turn keeping his campaign promises with his executive orders to “not really wanting unity” is the disingenuous bullshit that Fox News is trying to push.