For the general case please see Fit text into given box by adjusting the fontsize. For your specific case you could use the following way, which scales the content if required. I'm not saying that will give nice results in all cases.
Note that the use of minipage
modifies the \textwidth
so that length can be different at different places. Keep also in mind that later adjustbox
keys can effect earlier one because of this:
\documentclass{report}
\usepackage{fancybox}
\usepackage{adjustbox}
\newenvironment{myovalbox}{%
\noindent
\adjustbox{minipage=[c]{.45\textwidth},margin=1ex,max totalsize={\textwidth}{.7\textwidth},center=.5\textwidth,
env={minipage}[c][.35\textwidth]{.5\textwidth},
precode=\ovalbox}\bgroup
}{%
\egroup
}
\begin{document}
\begin{myovalbox}
This text is small enough to fit in the box.
\end{myovalbox}
\begin{myovalbox}
This text might be too large to fit into the (.35x.50)$\cdot$textwidth box,
in which case the font size should be decreased to make it fit.
\end{myovalbox}
\begin{myovalbox}
This text might be too large to fit into the (.35x.50)$\cdot$textwidth box,
in which case the font size should be decreased to make it fit.
This text might be too large to fit into the (.35x.50)$\cdot$textwidth box,
in which case the font size should be decreased to make it fit.
\end{myovalbox}
\begin{myovalbox}
This text might be too large to fit into the (.35x.50)$\cdot$textwidth box,
in which case the font size should be decreased to make it fit.
This text might be too large to fit into the (.35x.50)$\cdot$textwidth box,
in which case the font size should be decreased to make it fit.
This text might be too large to fit into the (.35x.50)$\cdot$textwidth box,
in which case the font size should be decreased to make it fit.
\end{myovalbox}
\begin{myovalbox}
This text might be too large to fit into the (.35x.50)$\cdot$textwidth box,
in which case the font size should be decreased to make it fit.
This text might be too large to fit into the (.35x.50)$\cdot$textwidth box,
in which case the font size should be decreased to make it fit.
This text might be too large to fit into the (.35x.50)$\cdot$textwidth box,
in which case the font size should be decreased to make it fit.
This text might be too large to fit into the (.35x.50)$\cdot$textwidth box,
in which case the font size should be decreased to make it fit.
This text might be too large to fit into the (.35x.50)$\cdot$textwidth box,
in which case the font size should be decreased to make it fit.
This text might be too large to fit into the (.35x.50)$\cdot$textwidth box,
in which case the font size should be decreased to make it fit.
\end{myovalbox}
\end{document}

\small
or adjust the height of the boxes.%
behind\ovalbox{
. As it is now it inserts an extra space there.