If you want to pretty indent the heredoc contents so that they are indented within the if clause, you can get most of the way there with the following code:

if (1) {
  (my $sOutput = <<'OUTPUT') =~ s/^\s+|\n(?!\s+\n)//gm;
    Today is Monday, my favorite day of the week.
    It is my favorite day because Jerry said "Monday
    is the best day of the week".  Tuesday is my second-favorite day.
    Why can't all days be as great as Monday?  Who knows.





    This is a second paragraph.
OUTPUT
  print "$sOutput\n";
}
[download]

which outputs

Today is Monday, my favorite day of the week.It is my favorite day bec
+ause Jerry said "Mondayis the best day of the week".  Tuesday is my s
+econd-favorite day.Why can't all days be as great as Monday?  Who kno
+ws.
This is a second paragraph.
[download]

You'll still need to keep OUTPUT at the start of the line (unless you chose to use whitespace in your end of here-doc marker as JavaFan suggests below), but at least you can indent the remainder of the text. The regular expression s/^\s+|\n(?!\s+\n)//gm removes leading whitespace on all lines. It merges together all lines that have only 1 newline between them and collapses a run of blank lines into a single newline. If instead you want to keep the line breaks exactly as shown in the heredoc, you can use a slightly different regular expression: s/^[^\S\n]+//gm, which results in the output:

Today is Monday, my favorite day of the week.
It is my favorite day because Jerry said "Monday
is the best day of the week".  Tuesday is my second-favorite day.
Why can't all days be as great as Monday?  Who knows.





This is a second paragraph.
[download]

For more information and other neat tricks you can do with here-documents, see perlop and search for "here-doc".

Best, beth

Update 1: added example that preserves line breaks.

Update 2: corrected my post with a parenthetical comment refering to JavaFan's post below.