No need to guess; use minipage instead of \parbox and remove the \mbox:
\documentclass{article}
\usepackage{enumitem,calc}
\begin{document}
Some text, Some text, Some text, Some text, Some text, Some text,
Some text, Some text, Some text, Some text, Some text, Some text
\begin{enumerate}
\item This is a line
\begin{minipage}[t]{\textwidth-\labelwidth-\labelsep-\widthof{This is a line}}
\begin{enumerate}[label=(\textit{\roman*})]
\item Text 1 Text 1 Text 1 Text 1 Text 1 Text 1 Text 1 Text 1 Text 1 Text 1 Text 1 Text 1
\item Text 2 Text 2 Text 2 Text 2 Text 2 Text 2 Text 2 Text 1 Text 1 Text 1 Text 1 Text 1
\end{enumerate}
\end{minipage}
\end{enumerate}
\end{document}

A better definition that allows for nesting at every level; but keep in mind that nesting several enumerations is bad style.
\documentclass{article}
\usepackage{showframe} % just for showing the page margins
\usepackage{enumitem,calc}
\newenvironment{xenumerate}[1]
{\begin{minipage}[t]{\linewidth-\widthof{#1}}
\begin{enumerate}[label=(\textit{\roman*})]}
{\end{enumerate}\end{minipage}}
\begin{document}
Some text, Some text, Some text, Some text, Some text, Some text,
Some text, Some text, Some text, Some text, Some text, Some text
\begin{enumerate}
\item This is a line
\begin{xenumerate}{This is a line}
\item Text 1 Text 1 Text 1 Text 1 Text 1 Text 1 Text 1 Text 1 Text 1 Text 1 Text 1 Text 1
\item Text 2 Text 2 Text 2 Text 2 Text 2 Text 2 Text 2 Text 1 Text 1 Text 1 Text 1 Text 1
\end{xenumerate}
\item Text text text text text text
\begin{enumerate}
\item Text Text Text Text
\begin{xenumerate}{Text Text Text Text}
\item Text 1 Text 1 Text 1 Text 1 Text 1 Text 1 Text 1 Text 1 Text 1 Text 1 Text 1 Text 1
\item Text 2 Text 2 Text 2 Text 2 Text 2 Text 2 Text 2 Text 1 Text 1 Text 1 Text 1 Text 1
\end{xenumerate}
\item End of the story
\end{enumerate}
\end{enumerate}
\end{document}

Version with an optional argument for changing the label
The default label is label=(\textit{\roman*}) as before, but you can change it as you please.
\documentclass{article}
\usepackage{showframe}
\usepackage{enumitem,calc}
\newenvironment{xenumerate}[2][label=(\textit{\roman*})]
{\begin{minipage}[t]{\linewidth-\widthof{#2}}
\begin{enumerate}[#1]}
{\end{enumerate}\end{minipage}}
\begin{document}
Some text, Some text, Some text, Some text, Some text, Some text,
Some text, Some text, Some text, Some text, Some text, Some text
\begin{enumerate}
\item This is a line
\begin{xenumerate}{This is a line}
\item Text 1 Text 1 Text 1 Text 1 Text 1 Text 1 Text 1 Text 1 Text 1 Text 1 Text 1 Text 1
\item Text 2 Text 2 Text 2 Text 2 Text 2 Text 2 Text 2 Text 1 Text 1 Text 1 Text 1 Text 1
\end{xenumerate}
\item Text text text text text text
\begin{enumerate}
\item Text Text Text Text
\begin{xenumerate}[label=(\arabic*)]{Text Text Text Text}
\item Text 1 Text 1 Text 1 Text 1 Text 1 Text 1 Text 1 Text 1 Text 1 Text 1 Text 1 Text 1
\item Text 2 Text 2 Text 2 Text 2 Text 2 Text 2 Text 2 Text 1 Text 1 Text 1 Text 1 Text 1
\end{xenumerate}
\item End of the story
\end{enumerate}
\end{enumerate}
\end{document}

\begin{document}to\end{document}). Without this it may be difficult for anyone to help you. I have no idea where the\widthofmacro comes from. – Ian Thompson May 09 '14 at 10:36\widthofis in thecalcpackage (I assumed this was widely used, so there wasn't a need to mention the package explicitly); since I used the tag "enumitem" in my question I implicitly assumed that this package also had to be added. – l7ll7 May 09 '14 at 16:56