It will affect foreign policy simply because it was an act of terrorism. Even though the bombers were American it still puts pressure on Barack Obama to fight terrorism in all areas, in all ways. It shows that terrorism is still a threat in the U.S. It is also not known whether they were alone or in contact with other terrorist groups. Therefore they have to be aware of every possible threats.
No, I do not think that as a result of the Boston bombings that Obama's foreign policy will be affected. I think that Obama will continue down the same course of using unilateral actions to prevent future wars, and will not try to engage Chechnya in a foreign war as a result of the bombings.
America can't be afraid of immigration; it's how we became a country to begin with. People with bad intentions can come from anywhere, and may have never done anything bad in the past that ruins their chance at citizenship. A better path would be to beef up security at public events.
It wouldn't make sense for this to effect Obama's foreign policy because Boston is an American city, not a foreign city. Also, my guess is that the bombers were probably Americans as well, and therefore would not even be linked to any foreign terrorist groups. It might make Obama look bad, but not on foreign policy.
The Boston bombing were tragic and were certainly an act of terror, however at the moment they appear to be the work of current U.S. Citizens. Although these citizens have a foreign background, it does not appear that their motives were fueled by international policies or the recent reelection of Barack Obama. While the bombings may not affect Mr. Obama's foreign policy, it may certainly affect domestic views in the U.S. Including the current debate of weapon regulation.