Changing all single quotes to be straight when within texttt

Here I redefine \texttt to make ' active and replace itself with \textquotesingle. The original definition is saved in \svtexttt.

EDITED to return ' to non-active status at the conclusion of a \texttt.

REEDITED to use letltxmacro, per egreg's suggestion.

REREEDITED to restore the originally defined ' after \texttt usage, so as not to interfere with math conversion to \prime (hat tip/mumbled curse to David).

\documentclass{article}
\usepackage{textcomp,lmodern,letltxmacro}
\LetLtxMacro{\svtexttt}{\texttt}
\catcode`'=\active %
\let\svprime'
\renewcommand\texttt{\catcode`'=\active \def'{\textquotesingle}\textttaux}
\newcommand\textttaux[1]{\svtexttt{#1}\gdef'{\svprime}\catcode`'=12 }
\catcode`'=12 %
\begin{document}
\svtexttt{That's life!}

versus

\texttt{That's life!}

Is ' active? No. 

Testing prime: $x' =dx/dt$
\end{document}

You could make ' active, but this has the big disadvantage that \texttt can no longer be used in the argument to another command.

\documentclass{article}
\usepackage{textcomp}
\usepackage{xparse}
\usepackage{etoolbox} % for robustify

\robustify\texttt

\let\originaltexttt\texttt
\newcommand\activatestraightquote{%
  \begingroup\lccode`~=`'
  \lowercase{\endgroup\let~}\textquotesingle
  \catcode`'=\active
}
\renewrobustcmd{\texttt}{%
  \begingroup\activatestraightquote
  \innertexttt
}
\newcommand{\innertexttt}[1]{\originaltexttt{#1}\endgroup}

\begin{document}

abc'def \texttt{abc'def} abc'def

\end{document}

A solution that's free from this problem.

\documentclass{article}
\usepackage{xparse}
\usepackage{textcomp}

\ExplSyntaxOn
\RenewDocumentCommand{\texttt}{m}
 {
  \group_begin:
  \tl_set:Nn \l_jmlarson_texttt_tl { #1 }
  \regex_replace_all:nnN { ' } { \c{textquotesingle} } \l_jmlarson_texttt_tl
  \ttfamily
  \tl_use:N \l_jmlarson_texttt_tl
  \group_end:
 }
\ExplSyntaxOff


\begin{document}

\section{abc'def \texttt{abc'def} abc'def}

abc'def \texttt{abc'def} abc'def

\end{document}

This can also be extended so as to treat also " and ''.

You can use package newtxtt with option straightquotes.

\documentclass{article}
\usepackage[straightquotes]{newtxtt}

\begin{document}

\section{abc'def \texttt{abc'def} abc'def}

abc'def \texttt{abc'def} abc'def

\texttt{`xyz', ``xyz'', "xyz"}

\end{document}

This method, by essence, replaces completely the typewriter font, naturally. In the example above it seems to fit not so bad with default serif font.