Daniel Griswold, trade economist at CATO Institute, describes (link) how American labor unions oppose the free-trade agreement between the U.S and Columbia although the U.S International Trade Commission's estimates show that the free trade agreement between the two countries would boost U.S exports by about $1 billion annually. The AFL complains that Columbia is an unworthy of an agreement because of violence levied on union members (link). This may sound politically feasible, but the background is certainly much different from what AFL complains. In fact, Daniel Griswold showed that Columbian unions are as safe as American unions against political violence (link).
Recall the basics of international trade, H-O-S theorem (link) explains that international trade occurs because of the differences in relative factor abundance, i.e. differences between labor/capital ratio. Thus, a country with relative abundance in labor shall export labor-intensive products while the second country shall export capital-intensive products and services. Consequently, relative wages in labor-abundant country are lower compared to those in capital-abudant country. Why? Because in a more developed capital-abundant country, labor is scarce and, hence, relative wage is higher.
The complete liberalization of trade between the U.S and Columbia would reward the relatively abundant factor in the U.S (capital) and reduce the real reward to less abundant factor (labor). Thus, in the short run, relative wages may decline. Note that the Columbian level of productivity is less than half of the U.S level. In the long run, however, relative wages shall not decline given a staggering difference in productivity between the U.S and Columbia.
As a interest group, AFL is protecting labor againist the short-run decline in relative wages. The hindrance of free trade, in fact, harms everyone. The U.S exporters would suffer the loss of one the key Latin American markets while the Columbian exporters wouldn't absorb the benefits of free trade. On the other hand, the greatest victims of protectionist trade policy are consumers. The consumers in the U.S would be denied the freedom of choice of Columbian imports while Columbian consumers would lose the variety of choices from the U.S at a lower price, following the abolition of tariff protection.