Does the H-1B visa program have the effect of reducing wages in the U.S In either the short or long term, does the H-1B visa program have the effect of reducing wages in the U.S. for U.S. citizens?
The program would increase the supply of labor to those specific sectors. As a result more foreign people would get into the sectors bidding the price down (lowering the wage). In addition, some Americans would not be able to get hired, that otherwise would have.

In addition, companies would become more profitable so more companies would be started and the reduced labor costs would be visible in other sectors, increasing labor demand elsewhere.

In the very long run free movement of labor is at least in theory more efficient than restricted movement, as people will more efficiently be able to navigate to the most efficient job locations available.