Matt Breunig at the People's Policy Project has been doing god's work, pointing out just how inconsistent the 'concerns' about the targetting of the payment are (the $2000 cheques are means-tested in case you didn't know that). Mainly, he points out that the targetting of the payments is no different than existing tax credits that everyone supports.

The program promises to pay $2,000 to every child and adult who lives in a tax unit with an adjusted gross income (AGI) that is below $75,000 (single filer), $112,500 (head of household filer), or $150,000 (married filer)

If the concern is the cost, it might make sense to improve the targetting of the cheques. But you wouldn't do by basing the targetting on who made over $75k last year, you would do it based on who lost income due to the pandemic. If this sounds familiar, it's because it's CERB.

Of course, it's questionable that the motivation is reducing the cost to begin with, because almost by definition, there just aren't that many high-income people and you really are only saving a few percent by cutting them out. So it's honestly a bit hard to understand what the opposition is based on.