It was huge. 250,000 people marched on the capital, from around the entire country, and approximately a quarter of them white. The Kennedy administration was attempting to push legislation to end discrimination. The purpose of the march, on the hundredth anniversary of the abolishment of slavery by President Lincoln, was to pressure the government into pushing the legislation forward and getting President Kennedy into signing it. There were hundreds of cameraman and radiomen, it was heavily covered by the media and broadcast nationally. In the following weeks, there was a very positive reception by the country because of the scale and importance of the event, and King's rhetoric. Dr. King's speech is considered one of the best speeches ever given, and is still studied by students around the world for the numerous rhetorical tactics employed.

So yes, it had an immediate impact and the entire country was very very aware of it.

Edit: source: Hansen, "The Dream: Martin Luther King, Jr, and the Speech that Inspired a Nation"

If I may hijack this topic slightly does anyone have any examples of what the response to the speech was from those opposed to the civil rights act?

I read somewhere that the famous 'dream' part of the speech had been used by King in many speeches before this one and that it was, in fact, a late inclusion to his speech that day. Can anyone elaborate?