Placing the enumerate in a minipage environment should do the trick
\noindent
\textbf{Part One - General}
\begin{enumerate}[leftmargin=*,topsep=1ex,itemsep=4ex,label={1.\arabic*}]
\item
\begin{minipage}[t]{\dimexpr0.30\textwidth\relax}
\raggedright
\textbf{SECTION INCLUDES}
\end{minipage}\hspace*{\fill}%'
\begin{minipage}[t]{\dimexpr0.70\textwidth-2em\relax}
\begin{enumerate}[align=left, label={.\arabic*}]
\item Work covered by Contract documents
\item Contract Method
\end{enumerate}
\end{minipage}
\item
\begin{minipage}[t]{\dimexpr0.30\textwidth\relax}
\raggedright
\textbf{THIS IS A LONGER TITLE}
\end{minipage}\hspace*{\fill}%'
\begin{minipage}[t]{\dimexpr0.70\textwidth-2em\relax}
\begin{enumerate}[align=left, label={.\arabic*}]
\item Work covered by Contract documents
\item Contract Method
\end{enumerate}
\end{minipage}
\end{enumerate}
I'm not sure why you're using the tabular environment.
You mentioned that you tried using a minipage. Be sure to pass the optional argument [t] to get the minipage to line up the baseline of its first line with the baseline of the text it's sitting on.
UPDATE: a much better solution
Here's something that is not so much a hack:
\documentclass{article}
\usepackage{fancyhdr}
\usepackage[head=41.68335pt]{geometry}
\usepackage{enumitem}
\usepackage{indentfirst}
\pagestyle{empty}
%% I use a box for your "title" and save its width in "\mytitlewidth"
\newlength{\mytitlewidth}
\newlength{\mytopsep}
\newsavebox{\mytitlebox}
%% and environment to handle your list
\newenvironment{enumwithinenum}[1]
{\setlength{\mytitlewidth}{\dimexpr0.30\textwidth\relax}%%'
\setlength{\mytopsep}{2ex}%%'
%% save the title in a box so we can access its height later to
%% use to adjust where the next enumerate begins.
\begin{lrbox}{\mytitlebox}%%'
\begin{minipage}[t]{\dimexpr\mytitlewidth\relax}
\raggedright\strut
\textbf{#1}
\par\xdef\tpd{\the\prevdepth}%%'
\end{minipage}%%'
\end{lrbox}%%"
\usebox{\mytitlebox}%%'
\vspace{-\dimexpr\dp\mytitlebox+\parskip+0.7\baselineskip+\mytopsep\relax}%%'
\begin{enumerate}[align=left,
label={.\arabic*},
leftmargin=\dimexpr\mytitlewidth+2em\relax,
topsep=\mytopsep,
]
}
{\end{enumerate}}
%-@-(1)---------------------------------------------------------------------
\begin{document}
\noindent
\textbf{Part One - General}
\begin{enumerate}[leftmargin=*,topsep=1ex,itemsep=4ex,label={1.\arabic*}]
\item \begin{enumwithinenum}{SECTION INCLUDES}
\item \strut Work covered by Contract documents
\item Contract Method
\item Contract Method
\item Contract Method
\item Contract Method
\item Contract Method
\item Contract Method
\item Contract Method
\item Contract Meth
\end{enumwithinenum}
\item \begin{enumwithinenum}{THIS IS A LONGER TITLE}
\item \strut Work covered by Contract documents
\item Contract Method
\end{enumwithinenum}
\end{enumerate}
\end{document}

This will work much better. No need to worry about multiple environments when you, in principle, only have one. The one thing that I think you will have to mind with this solution is placing a \strut on the first \item. Also, if you have any unusually tall objects on the first line of the enumerate, then the things will not line up as you need: but this shouldn't be a problem for most sorts of text.
\begin{tabular}etc not tables. I like the part .. I generate it with JavaScript:) – yannisl Jul 31 '13 at 20:45longtable? – yannisl Jul 31 '13 at 20:52\extrarowheightfor huge cells? – mafp Jul 31 '13 at 21:09