The omnibus bills aren’t blackmail, as much as a symptom of the failure of Congress to be able to do what it is supposed to: debate.

There is 1 funding bill per year which only requires a 50% vote instead of a 60% / 67% to pass that all other spending bills require.

Every member with a goal tries to attach it to the big annual funding bill. The bill becomes so large that nobody likes the bill as a whole, but everybody has something in it they will defend.

And the old filtering process (committees which recommend the content of bills) are dominated by majority party leadership. This is maybe the closest symptom to blackmail.