The two second idea has already been thought out and fictionalized in a Hugo Award winning tale by an author whose name I can't recall.
They started even simpler by building a "time window" first. You couldn't actually travel physically, but you could open a window into ANY time slice. Since the machine could be programmed to look "anywhen", 2 seconds ahead was just as easy as 1000 years behind. Even one tenth of a second was do-able. In fact that's just what everybody found to be the MOST interesting. Imagine peering into your neighboor's bedroom just one tenth of a second ahead of "real time". It was just like if you were peering "right now".
The machines were outlawed and destroyed forever. Never to be used again.
Hi Lee:
I was hopeing you would respond to this question. After read your past entries, I was disappointed in your answer. Perhaps you would like to try again. Do you not agree that any debate on TIME TRAVEL must begin with an understanding of the true nature of TIME?
You might like to go to Stephen Hawking's web site at WWW.hawking.org.uk as a source of data. He has posted some lectures about time. I read somewhere that he now supports the possibility of time travel, however I have not confirmed this from his web site.
I look forward to reading your thoughts on this subject.