"BigText" formating: how to adapt the fontsize to make all lines have the same width?

Here is a solution using adjustbox The vertical spacing between lines could be altered a bit, and the syntax could probably need some approvements.

Output

Code

\documentclass[11pt, margin=5pt]{standalone}
\usepackage{adjustbox}
\usepackage{xcolor}
\usepackage{pgffor}
\usepackage{helvet}

\definecolor{Pink}{HTML}{E22E3B}
\definecolor{Blue}{HTML}{0C2153}
\definecolor{DarkBlue}{HTML}{0C1C3B}
\definecolor{Red}{HTML}{C51E1F}

\setlength{\fboxrule}{4pt}
\setlength{\fboxsep}{10pt}

\newcommand{\BigWords}[1]{%
        \adjustboxset{min width=\linewidth, margin*=0.2em 1ex 0ex 0ex}%
        \foreach \i [count=\ni] in {#1}{%
                \ifnum\ni=1    
                        \adjustbox{}{\i}%
                \else
                        \\\adjustbox{}{\i}%
                \fi
        }\vspace{-1ex}%
}
\begin{document}
\fbox{%
    \begin{minipage}{15cm}
    \bfseries\sffamily
    \BigWords{SOME,TOTALLY,HIPSTER,QUOTE,ABOUT,LIFE}%
    \end{minipage}%
}%
\hspace{2em}%
\setlength{\fboxrule}{0.5pt}%
\fbox{%
    \begin{minipage}{20cm}
    \bfseries\sffamily
    \BigWords{
    \textcolor{Pink}{RUN},
    \textcolor{Blue}{LIKE},
    \textcolor{DarkBlue}{RYAN},
    \textcolor{Red}{GOSLING},
    \textcolor{Pink}{IS WAITING},
    \textcolor{Blue}{FOR YOU},
    \textcolor{DarkBlue}{AT THE},
    \textcolor{Red}{FINISH LINE},
    \textcolor{Pink}{(WITH A PUPPY)}%
    }%
    \end{minipage}%
}
\end{document}

An implementation with expl3 for a cleaner syntax:

\documentclass{article}
\usepackage{xparse}

\ExplSyntaxOn
\NewDocumentCommand{\bigtext}{mm}
 { % #1 = width, #2 = text, with \\ to separate lines
  \ebo_bigtext:nn { #1 } { #2 }
 }

\seq_new:N \l_ebo_bigtext_text_seq
\box_new:N \l_ebo_bigtext_line_box

\cs_new_protected:Nn \ebo_bigtext:nn
 {
  \begin{minipage}{#1}
  \baselineskip=-\maxdimen \lineskip=4pt
  \seq_set_split:Nnn \l_ebo_bigtext_text_seq { \\ } { #2 }
  \seq_map_inline:Nn \l_ebo_bigtext_text_seq
   {
    \hbox_set:Nn \l_ebo_bigtext_line_box { ##1 }
    \box_resize_to_wd:Nn \l_ebo_bigtext_line_box { \textwidth }
    \box_use:N \l_ebo_bigtext_line_box
   }
  \end{minipage}
 }
\ExplSyntaxOff

\begin{document}

\noindent
\bigtext{15em}{SOME \\ TOTALLY \\ HIPSTER \\ QUOTE \\ ABOUT \\ LIFE}
\quad
\sffamily
\bigtext{15em}{SOME \\ TOTALLY \\ HIPSTER \\ QUOTE \\ ABOUT \\ LIFE}

\end{document}

Spaces around \\ are ignored.

One might add an optional argument to set the vertical space between lines, in the macros above set to 3pt.

---

With XeLaTeX, but it needs a further refinement for the case when the line has a single letter:

\documentclass{article}
\usepackage{xparse,l3regex}
\usepackage{fontspec}

\ExplSyntaxOn
\NewDocumentCommand{\bigtext}{mm}
 { % #1 = width, #2 = text, with \\ to separate lines
  \ebo_bigtext:nn { #1 } { #2 }
 }

\seq_new:N \l_ebo_bigtext_text_seq
\box_new:N \l_ebo_bigtext_line_box
\tl_new:N \l_ebo_bigtext_line_tl

\cs_new_protected:Nn \ebo_bigtext:nn
 {
  \begin{minipage}{#1}
  \baselineskip=-\maxdimen \lineskip=4pt
  \seq_set_split:Nnn \l_ebo_bigtext_text_seq { \\ } { #2 }
  \seq_map_inline:Nn \l_ebo_bigtext_text_seq
   {
    \hbox_set:Nn \l_ebo_bigtext_line_box { \ebo_bigtext_remsb:n { ##1 } }
    \box_resize_to_wd:Nn \l_ebo_bigtext_line_box { \textwidth }
    \box_use:N \l_ebo_bigtext_line_box
   }
  \end{minipage}
 }
\cs_new_protected:Nn \ebo_bigtext_remsb:n
 {
  \tl_set:Nn \l_ebo_bigtext_line_tl { #1 }
  \regex_replace_once:nnN { \A(.) } { \c{ebo_kleft:n}\cB\{\1\cE\} } \l_ebo_bigtext_line_tl
  \regex_replace_once:nnN { (.)\Z } { \c{ebo_kright:n}\cB\{\1\cE\} } \l_ebo_bigtext_line_tl
  \tl_use:N \l_ebo_bigtext_line_tl
 }
\cs_new_protected:Nn \ebo_kleft:n
 {
  \kern-\XeTeXglyphbounds1~\the\XeTeXcharglyph`#1 #1
 }
\cs_new_protected:Nn \ebo_kright:n
 {
  #1\kern-\XeTeXglyphbounds3~\the\XeTeXcharglyph`#1
 }
\ExplSyntaxOff

\begin{document}

\noindent
\bigtext{15em}{SOME \\ TOTALLY \\ HIPSTER \\ QUOTE \\ ABOUT \\ LIFE}
\quad
\sffamily
\bigtext{15em}{SOME \\ TOTALLY \\ HIPSTER \\ QUOTE \\ ABOUT \\ LIFE}

\end{document}

Here's one option, just using resizebox

\documentclass{article}
\usepackage{graphicx}
\begin{document}
\newlength\foo
\setlength\foo{15em}
\noindent
\resizebox{\foo}{!}{SOME}\\
\resizebox{\foo}{!}{TOTALLY}\\
\resizebox{\foo}{!}{HIPSTER}\\
\resizebox{\foo}{!}{QUOTE}\\
\resizebox{\foo}{!}{ABOUT}\\
\resizebox{\foo}{!}{LIFE}\\
\end{document}

It's inelegant and cumbersome. But it's a proof of concept. This could be combined with the answers to this question for a more automatic solution.