It wasn't just the media that condemned his initial response, it was a heavy bipartisan response to it. Heck, his daughter responded in a way that was more sppropriate. As for the slow walk part, putting that in the title is certainly milking a little, but the fact is that he took over two days to come up with a better response.
The thing with Trump is that he is fully aware that anyone who is a democrat probably hates him, not to mention people who think it's just cool to make fun of him. In conclusion, he can't really afford it to pi** off his own supporters. This whole "slow walk" thing was the only thing he could do and he did a very smart job at holding his own ground.