Depending on what you are really trying to achieve, here are several possibilities:
\documentclass[a4paper,12pt,oneside]{article}
\usepackage[english]{babel}
\usepackage{tikz}
\usepackage{pgf}
%\usetikzlibrary{shapes,arrows,positioning,calc,threeparttable}
\usepackage{tabu}
\usepackage{hyperref}
\usepackage{longtable}
\usepackage{array}
\usepackage{multirow,tabularx,booktabs}
\parskip 1em
\begin{document}
\noindent\hrulefill
Tiny to get specified text layout
{\centering\tiny\begin{tabular}{cc}
\textbf{Text A:} & \textbf{Text B:} \\
\parbox[t]{.45\textwidth}{\centering ``Lorem ipsum dolor sit amet,
consectetuer adipiscing elit, sed diam
nonummy nibh euismod tincidunt ut laoreet dolore magna aliquam erat
volutpat.''} &
\parbox[t]{.45\textwidth}{\centering``Lorem ipsum dolor sit amet,
consectetuer adipiscing elit, sed diam
nonummy nibh euismod tincidunt ut laoreet dolore magna aliquam erat
volutpat.''} \\
\end{tabular}\par}
Normalsize
{\centering\begin{tabular}{|c|c|}
\hline
\textbf{Text A:} & \textbf{Text B:} \\
\hline
\parbox[t]{.45\textwidth}{\centering ``Lorem ipsum dolor sit amet,
consectetuer adipiscing elit, sed diam
nonummy nibh euismod tincidunt ut laoreet dolore magna aliquam erat
volutpat.''} &
\parbox[t]{.45\textwidth}{\centering``Lorem ipsum dolor sit amet,
consectetuer adipiscing elit, sed diam
nonummy nibh euismod tincidunt ut laoreet dolore magna aliquam erat
volutpat.''} \\
\hline
\end{tabular}\par}
Without lines:
{\centering\begin{tabular}{cc}
\textbf{Text A:} & \textbf{Text B:} \\
\parbox[t]{.45\textwidth}{\centering ``Lorem ipsum dolor sit amet,
consectetuer adipiscing elit, sed diam
nonummy nibh euismod tincidunt ut laoreet dolore magna aliquam erat
volutpat.''} &
\parbox[t]{.45\textwidth}{\centering``Lorem ipsum dolor sit amet,
consectetuer adipiscing elit, sed diam
nonummy nibh euismod tincidunt ut laoreet dolore magna aliquam erat
volutpat.''} \\
\end{tabular}\par}
\end{document}

EDIT to show how to make the top box locally exceed the margin, per OP's request. I place it in a \makebox[\textwidth]{...} to achieve this, remembering to \noindent the \makebox. The margin extent is shown with the \hrulefill at the top of the page.
\documentclass[a4paper,12pt,oneside]{article}
\usepackage[english]{babel}
\usepackage{tikz}
\usepackage{pgf}
%\usetikzlibrary{shapes,arrows,positioning,calc,threeparttable}
\usepackage{tabu}
\usepackage{hyperref}
\usepackage{longtable}
\usepackage{array}
\usepackage{multirow,tabularx,booktabs}
\parskip 1em
\begin{document}
\noindent\hrulefill
Footnotesize with margins exceeded to get specified text layout
\noindent\makebox[\textwidth]{\footnotesize\begin{tabular}{cc}
\textbf{Text A:} & \textbf{Text B:} \\
\parbox[t]{.6\textwidth}{\centering ``Lorem ipsum dolor sit amet,
consectetuer adipiscing elit, sed diam
nonummy nibh euismod tincidunt ut laoreet dolore magna aliquam erat
volutpat.''} &
\parbox[t]{.6\textwidth}{\centering``Lorem ipsum dolor sit amet,
consectetuer adipiscing elit, sed diam
nonummy nibh euismod tincidunt ut laoreet dolore magna aliquam erat
volutpat.''} \\
\end{tabular}}
Normalsize
{\centering\begin{tabular}{|c|c|}
\hline
\textbf{Text A:} & \textbf{Text B:} \\
\hline
\parbox[t]{.45\textwidth}{\centering ``Lorem ipsum dolor sit amet,
consectetuer adipiscing elit, sed diam
nonummy nibh euismod tincidunt ut laoreet dolore magna aliquam erat
volutpat.''} &
\parbox[t]{.45\textwidth}{\centering``Lorem ipsum dolor sit amet,
consectetuer adipiscing elit, sed diam
nonummy nibh euismod tincidunt ut laoreet dolore magna aliquam erat
volutpat.''} \\
\hline
\end{tabular}\par}
Without lines:
{\centering\begin{tabular}{cc}
\textbf{Text A:} & \textbf{Text B:} \\
\parbox[t]{.45\textwidth}{\centering ``Lorem ipsum dolor sit amet,
consectetuer adipiscing elit, sed diam
nonummy nibh euismod tincidunt ut laoreet dolore magna aliquam erat
volutpat.''} &
\parbox[t]{.45\textwidth}{\centering``Lorem ipsum dolor sit amet,
consectetuer adipiscing elit, sed diam
nonummy nibh euismod tincidunt ut laoreet dolore magna aliquam erat
volutpat.''} \\
\end{tabular}\par}
\end{document}

\parallelcan be used – Apr 21 '14 at 16:56