\documentclass{article}
\newlength{\varwidth}
\newenvironment{varpage}[1]
   {\settowidth{\varwidth}{#1}\begin{minipage}{\varwidth}}
   {\end{minipage}}
\begin{document}
\noindent
\begin{varpage}{`As wide as this sample text'}
  The width of this \texttt{minipage} environment is equal to that of the
  text\\
  `As wide as this sample text'\\
  as to seen here,
\end{varpage}\qquad
\begin{varpage}{`narrow sample text'}
  followed by the smal\-ler \texttt{minipage} environment of the width equal
  to the text:\\
  `narrow sample text'
\end{varpage}
\end{document}