Free trade helps to spread democractic ideals. This is the idea presented in a small article from the CATO Institute called Trade, Democracy, and the War on Terror. The article explains that as trade and globalization have spread throughout the last 30 years so have democracy and policitcal freedoms. Nations that have submited to trade reforms in recent years are more likely to expand their citizens' political and social freedoms.
If the United States government wants to spread democracy it should increase trade. It might be more effective to increase trade than to increase military pressure on most countries. Maybe the saying should be "the dollar is mightier than the sword."