Paint self out of corner
It's correct, or at least not incorrect. Because of its distance from the subject, you pretty much have to hyphenate "tax-cut," ugly as it is, just so it's clear that you're talking about something "tax-cut" modifies and not a cut in taxes themselves. But whether you're counting words or picas, the hed's three-quarters over before you get the subject out of the way.
The hed writer (or the slot; as Lovecraft implied, the solution is always clearer when you aren't the one in the maze) needed to think like a flight attendant: Remember, the nearest exit may be behind you. Stop counting the distance from the hyphenated compound to the subject noun and turn the whole thing around:
Final votes likely today
on tax cut, budget, DOT
It's simpler, it takes the hyphen question off the table, and it gets to the point at the outset.
Speaking of Lovecraft, this just in from The Ridger and too good not to spread more widely:
Ya! Ya! We await a good old-fashioned platform fight at the convention.