In the long-run, it would get passed onto consumers. But one of the nice parts about this, is how its easily avoidable tax(parking demand is price elastic, IE - people tend to look for alternatives, and luckily in downtown people do have alternatives such as RTA), and there won't be a huge shock to the consumer at first since parking prices would slowly increase over time.
On the demand side, a parking tax in a downtown core is more of a proxy way to tax car commuters. Parking fees will go up over time. It has the side benefit of nudging people away from driving, which has negative externalities(pollution, congestion). This moves them to more desirable forms of transportation, such as mass transit.
On the supply side, a parking tax has a tendency to tax discourage building of new parking lots/garages. Specifically, it will make surface lot financials much less attractive, and may spur development of surface lots into 'better' uses.
An increase in the parking tax from 8% to 37.5% would increase revenue by $41M/year for the City of Cleveland. This would be something like an increase in revenues by 8%.
Assuming somehow the county did a county-wide parking tax, we could see that $41M go to fund the RTA. That would increase RTAs budget by 13.3%. They need something like $140M to get matching fed funds for replacement railcars. In a little over 3 years, this tax alone could fund those cars.
Now, Cleveland doesn't need to go all the way to 37.5%, but is going to 12% or 15% really that crazy? The city is discussing increasing income taxes to 2.5%, which I think is way more drastic - it hits everyone. There's no way to avoid it(except move/not work in Cleveland).
(Yet again, I don't have enough posts so it's not letting me post links to sources for some of the numbers above, but a site called rebuildcle will have an article on the parking tax)