In no order, and just off the top of my head...
Cost: It's expensive. According to the link, $1200 per month per adult, plus Medicare for all, comes at a cost of 4.4 Trillion a year. However, this year the Federal Government's TOTAL revenue was about 2.75 Trillion. So, under this plan, before we have even spent a penny on Defense or Education or any of the other necessary programs, we would be running 1.5 Trillion deficits, and that's not even close to sustainable.
If we wanted to do this we would need massive tax hikes on the top earners.
Inflation I am not smart enough to know the answer, but I suspect that this much cash entering the economy would cause a great deal of price inflation, at least until things stabilized, and that this inflation would have a significant impact on the actual value of this subsidy. How this played out over the long term I could not begin to say.
Taxes At a time when the Feds need every dime to try and fund this massive spending program, we would predictably see a great many people voluntarily cutting their own hours and using their subsidy, and companies cutting pay under the premise that the subsidy makes up the difference. This would include the middle class, the group currently getting squeezed. If a family deliberately works fewer hours and uses their subsidy to compensate, or their employer cuts their pay using the subsidy as an excuse, in either case that family isn't going to be earning as much taxable income.
In other words, the entire tax code would need to be redesigned in order to extract the necessary money from the top, and particularly from Capital Gains.