Unfortunately my server keeps cutting me off, thus I have not been able to surf much. I do not know how many weeks it took the SS Republic to cross the ocean from England to America, but it would have been between 3 weeks and 6 weeks. I did manage to discover that the "North German Lloyd Packet Line" sailed out of Bremen so we can cross their Norddeutcher Loyd ships off the list that carried your ancestors to England. Here is a website which explains the main transatlantic companies operating routes between German ports and North America was the North German Lloyd (Norddeutcher Loyd) and the Hamburg America Line (HAPAG), which we can also cross off the list.
The website also shows pictures of Hamburg dockside which your Klug family will have walked on..
http://www.norwayheritage.com/p_shiplist.asp?co=haaml
Rena