'No ifs, no butts' was the headline for a story discussed on daytime TV show The Wright Stuff.  The story was about the forthcoming introduction of plain pack cigarettes in the UK.  

Usually we say, "No ifs, no buts", or "No ifs and buts", to stop any argument when you want someone to do something.  

For example: Do your homework tonight, no ifs and buts.

In the headline, the word but has been replaced with butt, for cigarette butt; the name given to the remains of a cigarette after smoking.