The European Union and the United States will always be aligned and on good terms. While I am sure there are those who would prefer to EU to remain in its current form, the relationship will remain strong. The greatest threat to the Western world is ISIS and the EU and United States will remain committed to the defeat of terrorist groups. All parties understand the amount of cooperation it will take to achieve this goal.
No, I do not think the United Kingdom leaving the European Union will affect EU relations with the United States because countries in the EU know that The United States of America is one of the greatest countries in the world and that any major military or economic plan requires America's involvement. I believe that America's relationship with the EU will not change and that the EU and USA will continue to work together.
The United Kingdom's vote on whether or not to stay in the European Union is unlikely to have any baring on the former's relations with the United States. This is an internal matter in Europe. We have a good relationship with most of Europe. We will continue to trade and have diplomatic relations with both.
The UK will always be allies with the US. This is because of the historical relationship between the two countries. I believe the separation from the EU will affect the UK vs other European countries rather than America. The US should, in fact, be more supportive of the UK if they choose to make this transition.