In 1966, there was a a movement to apparently build a tunnel from Biscayne Boulevard (by where the Intercontinental is) to go under the river, under the then Dupont Plaza and into Brickell and Brickell Point. The problem then was most likely that there wasn’t a need for it. Its a relatively short distance and the SE 1st Avenue and Miami Avenue bridges pretty much handle the area’s current needs.
The topic was again revisited in a March 2006 study, which again didn’t find a neccessity and that the substantial costs would not justify the minimal benefits to traffic flow. Here’s the exact wording of the study:
Miami River Tunnel Feasibility Study – This study assessed the construction feasibility and environmental and traffic impacts of a tunnel connection under the Miami River to connect the Downtown Central Business District and Brickell areas unimpeded by marine navigation. The feasibility report was completed by RS&H in March 2006 and documents the substantial cost associated with the right-of-way impacts and construction of the project in comparison to the marginal benefits to traffic flow and mobility.