Since when do conservatives like when the government charges big taxes on stuff you want to buy (tariffs)? Screw that.
Just a guess, I think the first hundred years or so of this country, our government was pretty conservative. The government which was financed almost completely by tariffs.
Reagan slapped a tariff on Japanese motorcycles. They were dumping their motorcycles in the US at below cost to drive Harley out of business. After that, they intended to jack up the price of their motorcycles.
Whenever the US oil industry gets going, the Saudis pump and drive the price down until all the US manufacturers go out of business. Then they shut down the spigot and jack the price again. If you just say, "I support free trade," other nations will eat your lunch. The simplest way, and one which Japan used a lot, was to have the government funnel money to companies so they could sell at a loss until competitors went out of business.
OTOH, just throwing up tariffs allows US manufacturers to get frikkin lazy and form a cartel (Ford, GM, Chrysler before the Japanese and Germans got in.)
People negotiating trade deals have to be sharp, and they have to be people who won't sell their country down the river for a pitifully small bribe. You can't say, "I'm for free trade" and walk off, expecting everyone else to play fair.