Is there a srcset equivalent for css background image

You can use media queries for your purpose. It's easy as this:

.mycontainer {    
    background-image:url("img/image-big.jpg"); // big image   
}

@media(max-width: 768px){
   .mycontainer {
        background-image:url("img/image-sm.jpg"); // small image  
    }
}

And I think it works on every browser who support media queries ;)

image-set is the equivalent CSS feature. We should add equivalent srcset functionality (defining resources according to their dimensions) to the spec.

Currently implemented in all major Browsers (Firefox, Chrome, Safari, Edge) with the -webkit- prefix. Safari only supports supports the x descriptors.

Another approach, which is quite frankly more robust, would be to adapt the characteristics and options of background images to an image with the srcset attribute.

To do this, set the image to be width: 100%; height: 100%; and object-fit: cover or contain.

Here is an example:

.pseudo-background-img-container {
  position: relative;
  width:400px;
  height: 200px;
}
.pseudo-background-img {
  position: absolute;
  top: 0;
  left: 0;
  width: 100%;
  height: 100%;
  object-fit: cover;
}

<div class="pseudo-background-img-container">

<img class="pseudo-background-img" src="https://cdn3.tnwcdn.com/wp-content/blogs.dir/1/files/2016/12/Keep.jpg" srcset="https://cdn0.tnwcdn.com/wp-content/blogs.dir/1/files/2016/12/Keep.jpg 640w, https://cdn0.tnwcdn.com/wp-content/blogs.dir/1/files/2016/12/Keep-280x175.jpg 280w, https://cdn0.tnwcdn.com/wp-content/blogs.dir/1/files/2016/12/Keep-432x270.jpg 432w, https://cdn0.tnwcdn.com/wp-content/blogs.dir/1/files/2016/12/Keep-216x135.jpg 216w" sizes="(max-width: 640px) 100vw, 640px">

</div>

This may not be the best approach for everyone but I imagine it will get most the desired results without any javascript workaround.

Pretty sure that:

background: -webkit-image-set( url('path/to/image') 1x, url('path/to/high-res-image') 2x );

works the same way. The browser will examine the images, see which fits best and will use that one.