Would the U.S. government gain any advantage from using tariffs or quotas to restrict imports?

Answer 1

No. One prime example is the Canadian lumber deal. The U.S. has repeatedly reneged on the original deal and is now taking Canada to court again for their own gain. In the long run it is a troublesome thing for the U.S. because the world economy is growing towards other nations aside from the U.S.
What the U.S. is doing will allow countries of Europe,Africa,and Asian nations to see how they work with their foreign policies regarding trade in tariffs and quotas
The economic market is not so dependant on the U.S. as it used to be. With East India, and China opening up to trade faster than we can give to them; then you can bet that is an extra two billion people to market to. With the U.S. only having a market of three hundred million who do you think will get trade, and imports from the other nations of the world?
Not the U.S.A.
The U.S. government has a reputation of making deals in trade then taking what they want from it, then giving what THEY THINK is a good deal.
Admitted that all countries do that; but not nearly to the extent of the U.S. government.

Answer 2

There is a short-term gain -- the government gets revenues from these restrictions.

But, over time, the protected firms will raise their prices and be unproductive. So, over the longer term, both the US government and the US consumer is worse off.

Answer 3

No. The problem is political parties and politicians have something to gain buy it. Usually in the way of support and money that helps them get elected.