To do a task, like vacuuming the house, without making any excuses.
Oftentimes, when a person makes an excuse on why they don't want to do something, these excuses involve the conjectures if, and, or but. For example: a parent might tell their child to take out the garbage, but the child comes up with an excuse and says: "But I'm in the middle of something, I'll do it later." Or perhaps they are asked to do the dishes, but they say: "It's almost bed time and I'm tired, what if I did the dishes tomorrow?" Thus, someone who is tired of hearing excuses might say they want something to be done, and no 'if, ands, or buts' about it. No excuses, in other words.
The phrase is at least over 150 years old, as it has been used during the 1800s. For instance, the expression was written in the New York Daily Times newspaper from the year 1854:
"No ifs or ands or buts about it."
* The windows in Bob's house are dirty, and he's been putting off cleaning them for a few days now. Today, however, Bob is going to clean the windows, no ifs, ands, or buts.
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Note: For many common idioms, their origins cannot be said with a certainty. Sometimes, then, what's provided are theories as to how a phrase may originated. If no theories are listed, then I'll usually try to provide a quote of the earliest known citation of a phrase.
In addition, quotes that contain a phrase may be taken from old newspapers, poems, or books that were written centuries ago. Just because I quote an old newspaper from, say, 1750, this does not mean the idiom originates from that year. The quote is there to give you an idea on at least how old the the idiom is.