With longtable
you can do this, if tabu
has broken it then that's a problem with tabu
:-)

\documentclass[a4paper]{article}
\usepackage{longtable}
\usepackage{lipsum}
\begin{document}
\section{This is the original textwidth.}
\lipsum[1]
\section{This is the width I need for my longtabu}
\setlength\LTleft{-1in}
\setlength\LTright{-1in}
\begin{longtable}{@{\extracolsep{\fill}}*{13}{|r}|@{}}
01 & 02 & 03 & 04 & 05 & 06 & 07 & 08 & 09 & 10 & 11 & 12 & 13 \\
01 & 02 & 03 & 04 & 05 & 06 & 07 & 08 & 09 & 10 & 11 & 12 & 13 \\
01 & 02 & 03 & 04 & 05 & 06 & 07 & 08 & 09 & 10 & 11 & 12 & 13 \\
01 & 02 & 03 & 04 & 05 & 06 & 07 & 08 & 09 & 10 & 11 & 12 & 13 \\
\end{longtable}
\end{document}
Here is a minimally-disruptive solution using just longtable
as suggested by Mike Renfro:
\documentclass{article}
\usepackage{longtable}
\begin{document}
\begin{longtable}{c|c|c|cp{.3\linewidth}c|c|c|c}
\multicolumn{4}{c}{Table \thetable\ First Results} & \multicolumn{1}{c}{\stepcounter{table}} & \multicolumn{4}{c}{Table \thetable\ Second Results} \\
\cline{2-3}\cline{7-8}
& 28\% & 33\% & & & & 24\% & 64\% \\
& 22\% & 36\% & & & & 76\% & 22\% \\
& 58\% & 49\% & & & & 2\% & 8\% \\
& 4\% & 89\% & & & & 32\% & 55\%\\
\cline{2-3}\cline{7-8}
\end{longtable}
\end{document}

However, it may be better to follow the advice in the booktabs documentation and add a bit more spacing, dispensing with vertical rules:
\documentclass{article}
\usepackage{array,longtable,booktabs}
\begin{document}
\begin{longtable}{cc>{\hspace*{.01\linewidth}}c<{\hspace*{.1\linewidth}}cc}
\caption{Results}\\
\toprule
\multicolumn{2}{c}{First Results} & & \multicolumn{2}{c}{Second Results}\\\midrule\endhead
\bottomrule\endfoot
28\% & 33\% & & 24\% & 64\% \\
22\% & 36\% & & 76\% & 22\% \\
58\% & 49\% & & 2\% & 8\% \\
4\% & 89\% & & 32\% & 55\%\\
\end{longtable}
\end{document}

But you might also think about how to set out the information. If everything is a % result, you might put this in the table caption and then present the first and second results as raw numbers. In this version, I also use the siunitx package to handle the numerical values nicely:
\documentclass{article}
\usepackage{array,longtable,booktabs,siunitx}
\begin{document}
\begin{longtable}{SS>{\hspace*{.01\linewidth}}c<{\hspace*{.1\linewidth}}SS}
\caption{Results (\%)}\\
\toprule
\multicolumn{2}{c}{First} & & \multicolumn{2}{c}{Second}\\\midrule\endhead
\bottomrule\endfoot
28 & 33 & & 24 & 64 \\
22 & 36 & & 76 & 22 \\
58 & 49 & & 2 & 8 \\
4 & 89 & & 32 & 55\\
\end{longtable}
\end{document}

Best Answer
The documentation says that one can use the optional argument
for getting left alignment for a single
longtable
. Useif you want left alignment for all
longtable
environments.