I believe their is money already set aside, by both Cuyahoga and the state, pledged to the stadium project. Now if we are talking new taxes, then that may be a problem, sure.
I know I read an article about Minnesota running a pull tab game for the new Vikings Stadium and that's likely to be the next thing the Browns do. There are other ways to do this other than simply having new taxes.
Truthfully, the city of Cleveland should be happy. The economic impact of losing the Browns is very slight, as tailgating downtown will likely still happen; at least for the ones that happen at bars. And now they don't have to justify money on a stadium and can use it for stuff they truly need, like schools and infrastructure that are both falling apart.