Immigration and tenure track in the United States I have plans to apply for some TT positions in the US. However, I'm Brazilian and I don't even have a visiting visa. I've never been to the US. 

Therefore the whole immigration process is mainly unknown to me, with the exception of a small amount of information I managed to gather online. 

Ignoring the CV, merits, etc, which I know play a decisive part in the TT hiring process, my question is : 


  How much the immigration hassle can change the outcome of the hiring process? 


Just to clarify further, I'm interested in the immigration factor only. Is it relevant? 

Of course, a foreign superstar would be good enough reason to overcome these obstacles, but I'm no superstar and I was wondering where they draw the line, if it is even worth to do the applications... (If you are extra curious, my scholar : https://scholar.google.com.br/citations?user=0D1ExLoAAAAJ)

Possibly related: Is it more difficult to score a Tenure Track position in the US when applying from outside?
I've taught at both large R1 universities and small liberal arts colleges. For the large R1s, we don't care -- we simply want the best person for the job, regardless of their nationality. R1s have very competent foreign scholar offices and lawyers who know how to do the proper visa paperwork.

At smaller schools, it's more difficult. Budgets are tighter and the provost has more say over searches. If there are two candidates that are almost equally ranked, then the provost may suggest one over the other for non-academic reasons. There may not even be approval for international airfare for job candidates at the interview stage. 

You have to remember that an H1B application will cost at least $10,00-$20,000 in lawyer's fees, staff time,  and application costs. The stack of paperwork for the Department of Labor certification itself is about 3 inches thick. Furthermore, even though there is an exemption, sometimes H1B applications can be very, very slow -- which means that an instructor hired in March might not be able to join the campus by August. This can be deadly for a small school that needs its faculty present.

tl;dr Be the absolute best candidate possible for the position and the visa status won't matter. Otherwise, it is a factor amongst other factors.