Under similar circumstances, I suspect there would be a clamor for war from both Republicans and Democrats. I do not think, however, that there is much of an analogy to be drawn between modern crises and the War of 1812. It involved geopolitical issues that were very specific to the late eighteenth and early nineteenth centuries, and the United States exercises such a degree of strategic hegemony over the Western Hemisphere today that I do not think most comparisons would be valid.
I agree with the above posts who thought that we would probably go to war. If the issues were similar, like impressment and unfair seizure of goods in the War of 1812, we would definitely defend ourselves. Can you imagine the headlines if some country just started high-jacking our ships and oil tankers, for example? Oh my. With our media coverage the way it is, people in the U.S. would call for action. The U.S. has never appreciated being pushed around.
I think that we would certainly go to war in such a situation. We can even see proof of it in some ways in our war against the Taliban. In 1812, we fought the British partly because they were stirring up Indian attacks against our settlers. In 2001, we attacked the Taliban because they had allowed Al Qaeda to train on their soil to attack us. It's a pretty similar thing.
In the interest of full disclosure, I tend to vote liberally and Democrat.
Americans today wouldn't stand for the treatment of fellow American traders any more than their ancestors did. If another nation was aggressively impressing our men and women (forcing them to serve in an armed force) and/or taking our shipments of goods, our government would absolutely take action. We care too much about our economy, too much about our well-being, to let that kind of aggression go unanswered.
There would be pressure from Congress and the public to "Save America"; the far-right of the Republican party would doubtlessly seize the opportunity to strike fear in Americans while the far-left liberal agenda would likely stay relatively quiet. It's an issue both sides can agree on -- American goods and people should be protected -- but the noise of one side would drown out the solutions of the other. Our new War Hawks would push for a declaration of war and there probably would be one. The president, however, would likely want to steer the nation to a more evident victory; the war of 1812 was such a wash!