Loop to fetch 3 post_thumbnail instances from 3 most recent custom post types named “portfolio”

Try this:

<?php get_header(); ?>
<div id="content" class="clearfix row">     
<article id="post-<?php the_ID(); ?>" <?php post_class('clearfix'); ?> role="article">
    <section id="work" class="row">      
        <div class="span3">
            <h3>Recent Work</h3>
            <p>Intro Lorem ipsum</p>
        </div>          
        <?php $args = array(
            'post_type'      => 'portfolio',
            'post_status'    => 'publish',
            'posts_per_page' => 3
        );
        $query = new WP_Query( $args );
        $porfolio_post_ids = array();
        if ( $query->have_posts() ) {
            while ( $query->have_posts() ) {
                global $post;
                $query->the_post();
                array_push( $porfolio_post_ids, $post->ID );
            }
        } ?>
        <div class="span6">
            <a href="https://wordpress.stackexchange.com/questions/48554/<?php echo get_permalink( $porfolio_post_ids[0] ); ?>">
                <?php echo get_the_post_thumbnail(  
                    $porfolio_post_ids[0] , 'medium' 
                ); ?> <!--Should be from custom post 'A' -->
            </a>
        </div>   
        <div class="span3">
            <a href="<?php echo get_permalink( $porfolio_post_ids[1] ); ?>" >
                <?php echo get_the_post_thumbnail(  
                    $porfolio_post_ids[1] , 'thumbnail' 
                ); ?><!--Should be from custom post 'B' -->      
            </a>    
            <a href="<?php echo get_permalink( $porfolio_post_ids[2] ); ?>">
                <?php echo get_the_post_thumbnail( 
                    $porfolio_post_ids[2] , 'thumbnail' 
                ); ?><!--Should be from custom post 'C' -->
            </a>  
        </div>

and don’t forget to set the thumbnail in functions.php as mentioned in David’s answer.

One more thing I noticed in your code: you said that your post type is “portfolio” and in the permalink you used single-project.php, but shouldn’t it be single-portfolio.php?