That would be a very unusual step - the last time a Senate parliamentarian was overruled was 45 years ago.
In addition, two D senators would be/are opposed to that for different reasons so even overruling would likely only get the Democrats to 48 votes potentially scuttling the whole rescue package.
In that article I linked to are quotes from both Pelosi and Schumer, claiming they want to see a $15 minimum wage. Biden is 'said' to be in favour of it too, as is Harris, or so she 'says'.
Maybe Harris overruling the parliamentarian would cause minor problems, but that aside; an executive order is still an option. Biden could sign one after his breakfast this morning, but he will not.
The truth of the matter is these people don't care about the American people. They can agree within literally days to find $800-$900B for what's sickeningly called the 'defence' budget though, and can always manage to agree to tax cuts for giant corporations, and Trillions of Dollars for banks in what's basically socialism, for banks.
They are paid servants of the powerful, blue or red, and an obstacle to the changes people need. It's pretty similar in the UK now, and the media - owned by oligarchs - is ready in both countries to cripple anyone who might stand in the way of the oligarch/corporate agendas.
Biden/Harris are just more of the same. No different to Obama, Trump etc.