Big Loop (>2000 posts) – Too big?

Hi, i got a blog with many articles.

$searchposts = get_posts('showposts=-1');
    foreach($searchposts as $searchpost) :
        $posttitle=$searchpost->post_title;
    endforeach;

I planned to create this very simple code to check if a given post-title exists.

But I have got > 2000 Articles (Video Rental Database) and I found out that I got a limit of ‘showposts = around 500’ .
Then the site seems to keep loading or something. Nothing happens.

If I decrease ‘showposts’, I get output, so the loop itself has to be okay, right?
Even if I delete following lines:

foreach($searchposts as $searchpost) :
        $posttitle=$searchpost->post_title;
    endforeach;

and I have only this one line:
$searchposts = get_posts('showposts=-1');

My site is stopping and nothing happens. Any code that is following after that line will not be processed.

What limit do I exceed ?

Is there a more ressource-saving method to query all post titles?
I certainly do not have to fill the $searchposts – variable with content, custom-fields, etc. Maybe directly access the database?