I would say it might be hard to *learn* multiple languages at once, because what you're actually learning is syntax, and it would be much easier to confuse the syntaxes whilst learning, while it is still "mushy". Over many years, learning many languages is not difficult at all in my opinion. The most challenging is learning a paradigm. Learning procedural programming is different than functional programming is different (somewhat) from OO of either flavor is different from MLs, etc. Once you've learned one language of a particular paradigm, in my opinion it is quite easy to learn another, because as Zortrium said, you learn the concepts while you're learning the syntax for the first language. From then on, it's just syntax, and that's pretty easy.
Every day I read and write:
C
Fortran 77/90/95 (in order of decreasing unpleasantness)
BASH
Perl
Java
SQL (mostly regular CRUD, occasionally pl/pgsql for functions, etc.)
Various UNIX tools (awk, sed, etc.)
If i'm perusing the code of my companies other product, javascript gets in the mix, too. This is not a comprehensive list of the languages I know... I regularly post Objective-C, Haskell ("regularly" may be an overstatement on this), Applescript (again, maybe not regularly), etc. on this forum. In school I worked with C++, MIPS ASM, x86 ASM, Prolog, LISP, etc.
The summary is:
No, it is not hard to be a programming language polyglot, but i would bite off one thing at a time. No use in confusing yourself. Once you've learned one thing (not mastered, just comfortable with its use), you can start learning something else.
-Lee