I get the difficulty but it's doable. A smart and savvy politician, who first galvanizes significant local support can get it done. For example, if the most vocal opponent is a former fire chief, perhaps Mansfield needs a new fire station and a few new trucks--lol.
Let's take a look at a place where it was done successfully. I believe the poster child for the process is the U of Minnesota.
The University pushed for a new on-campus stadium for football beginning in the fall of 2000, citing poor revenue and lack of a college football atmosphere at the off-campus Metrodome as their main reasons for wanting to move back on campus. (Sound familiar?)
The university concentrated on drafting a stadium proposal that would draw the support of state politicians.They went through the bumps and grinds of the legislative process and ultimately built this stadium (which seats 50,000).
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Construction started in 2006 and it opened in 2009. The total cost was $288M. (Today, I don't know, $400M?)
As a product of negotiations in the legislature, 52% was borne by the University and 48% by the State of Minnesota The University then sold naming rights to a large bank, received parking and concession revenue, charged a modest $25 fee per student and engaged in smart PR, They built a Native American Plaza and received a $14.5M donation from the local Mdewakanton tribe. (Notice any similarities for us here in CT?) They also built a Marching band facility next to the stadium for easy access. (we lack any band facility, unlike UMass, which has a great one.) UMinn raised a lot of money from music alumni and the music industry.
They were also savvy to put plaques in the stadium walls honoring every county in the state, since all of them contributed. And on and on and on.
We don't need a stadium that large, but UM's is a great place to start. As Mora says "hard things are hard"--but not impossible. Don't tell me it can't be done in CT.