I think that people view protectionism in the wrong way. If they gave subsidies to those same companies, I don't think most people that support protectionism would approve of that.
Protectionism doesn't just hurt the company exporting goods. It also hurts consumers in the importing country. Protectionism raises prices for the protected goods, because domestic companies face reduced competition therefore greater demand for their goods. That effectively is a small, indirect tax that each consumer in America has to pay, to prop up the profits of a business. It's corporate welfare disguised as nationalism.
The other problem is that US manufacturing isn't in danger. US manufacturing output has increased over time, and is still significantly larger than most of the world. Manufacturing jobs have decreased, but that's because the industry has matured. Just like agriculture jobs declined from 80% of the workforce in 1870 to less than 2% today not because we weren't farming, but because we didn't need that many farmers, manufacturing jobs are declining as a percentage of the workforce not because we aren't competitive at manufacturing, but because we don't need that many factory workers.
UN data on national GDPs split by sectors indicates that in 1994, US real manufacturing output was 1.5 trillion, while in 2014 US real manufacturing output was 2.9 trillion. The only year in that time period where US manufacturing output didn't grow was in 2008, at the height of the recession, where manufacturing output saw a slight decline. On the other hand, we saw significant job losses during that period, going from 16.9 million jobs to 12.3 million. Even if we implemented protectionist measures, we could, at best, slow that decline. In the long run manufacturing simply will not be as important in the US economy.
Likewise, people heavily overestimate our trade deficit. We have 2.35 trillion in real exports and 2.85 trillion in real imports. In other words, we export 21% more than we import. For comparison, in 1984, we imported 300 billion and exported 400 billion, or 33% more exports than imports. People say "the trade deficit is rising!", but the ratio of exports to imports is not some huge historical anomaly right now. Media like to use the numbers in a deceptive way to sell a story. "US manufacturing is doing p deece but it could be doing slightly better I guess, really the economy is just changing" is more complicated and less interesting than "CHINA SMASHING US IN MANUFACTURING CAN WE RECOVER???"