draw diagonal lines in div background with CSS

Solution that automatically scales to dimensions of an element would be usage of CSS3 linear-gradient connected with calc() as shown below. (There were some issues with Chrome in times of v30+ versions that this answer originally described but looks like they got resolved in the meantime and in v90+ it works as expected).

.crossed {
     background: 
         linear-gradient(to top left,
             rgba(0,0,0,0) 0%,
             rgba(0,0,0,0) calc(50% - 0.8px),
             rgba(0,0,0,1) 50%,
             rgba(0,0,0,0) calc(50% + 0.8px),
             rgba(0,0,0,0) 100%),
         linear-gradient(to top right,
             rgba(0,0,0,0) 0%,
             rgba(0,0,0,0) calc(50% - 0.8px),
             rgba(0,0,0,1) 50%,
             rgba(0,0,0,0) calc(50% + 0.8px),
             rgba(0,0,0,0) 100%);
}

<textarea class="crossed"></textarea>

You can do it something like this:

<style>
    .background {
        background-color: #BCBCBC;
        width: 100px;
        height: 50px;
        padding: 0; 
        margin: 0
    }
    .line1 {
        width: 112px;
        height: 47px;
        border-bottom: 1px solid red;
        -webkit-transform:
            translateY(-20px)
            translateX(5px)
            rotate(27deg); 
        position: absolute;
        /* top: -20px; */
    }
    .line2 {
        width: 112px;
        height: 47px;
        border-bottom: 1px solid green;
        -webkit-transform:
            translateY(20px)
            translateX(5px)
            rotate(-26deg);
        position: absolute;
        top: -33px;
        left: -13px;
    }
</style>
<div class="background">
    <div class="line1"></div>
    <div class="line2"></div>
</div>

Here is a jsfiddle.

Improved version of answer for your purpose.

You can use SVG to draw the lines.

.diag {
    background: url("data:image/svg+xml;utf8,<svg xmlns='http://www.w3.org/2000/svg' version='1.1' preserveAspectRatio='none' viewBox='0 0 100 100'><path d='M1 0 L0 1 L99 100 L100 99' fill='black' /><path d='M0 99 L99 0 L100 1 L1 100' fill='black' /></svg>");
    background-repeat:no-repeat;
    background-position:center center;
    background-size: 100% 100%, auto;
}

<div class="diag" style="width: 300px; height: 100px;"></div>

Have a play here: http://jsfiddle.net/tyw7vkvm