think on one's feet

大統領選で候補者が色々な表現をして、造語のようなものもあるようです。それに関する記事から拾います。
"Binders full of women"
Republican presidential nominee Mitt Romney uttered this phrase while thinking fast on his feet, in response to a voter's question during the second presidential debate.
Discussing how he tried to bring women into his cabinet while governor of Massachusetts, Romney stated, "I went to a number of women's groups and said, 'Can you help us find folks?' And they brought us whole binders full of women."
Biden: A bunch of 'malarkey'
The story of Romney's 'binders of women'
The Battle of Big Bird The remark spurred a political action committee to immediately mock Romney and set up bindersfullofwomen.com, dedicated to holding "Republican candidates accountable in this year's election and beyond."
http://edition.cnn.com/2012/10/19/politics/election-lingo/index.html?hpt=hp_c2

on one’s feetという表現です。「立っている状態で」（『ジーニアス英和辞典第４版』大修館）の他に、「（討論などに）即応できる、即席の」という意味があります。
ここでのthinking on his feetの意味です。「（立っている）その場に応じて考える」といったところから来ているのでしょうか。「考える」だけでなく、ためらわずに「答える」といったニュアンスも含まれている気がします。(Minnesota)