The normal Gaussian Blur is extremally slow in Blender. Consider using the Fast Gaussian Blur instead.
There's no direct way of using the effects strip of this effect, but there's a workaround.
Generally, Blender's Video Sequence Editor is an awesome tool; however, it lacks some functionality like some effects the Compositor has.
For example, as mentioned above, there is no Fast Gaussian Blur which is a lot faster than the normal Gaussian Blur with a minor margin of error (see this page for a comparison; it's not exactly the Blender's implementation, but it's pretty close). Furthermore, as far as my preferences go, I actually prefer the look of the Fast Gaussian to the normal Gaussian Blur.
In order to get the Compositor functionality for the VSE strips, you can use an add-on called Edit Strip With Compositor.
Note: There's another add-on mentioned in this thread called VSE to Compositor, but it doesn't work for Blender 2.76b.
So, let's get to it.
First, install the add-on. If you don't know how to do this, see this post.
After installing and enabling it, you can start using the compositing functionality for the VSE. Here's a demo of it; however, he uses the other add-on mentioned above in the note, but they're not that different.
To apply the effects from the Compositor to the VSE strip, you need to follow these steps:
- Select a video strip first (yes, unfortunately, you cannot apply the effects to the effects strips itself, but you can apply other effects on top of it).
- Press N on your keyboard to open the Properties panel.
- Scroll down in the Properties panel until you see the Edit strip with Compositor section.
- Click the Set master scene button.
- Check the Show options checkbox.
- In the Compositing, choose the Compositing option from the drop-down list.
- In the Editing Screen, choose the Video Editing option.
- Optionally, you can enable the Add Viewer option.
- Click the Create Comp from strip button on top of the section.
- Click the Edit Composition button.
- Now, this should look familiar. It should get you to the Blender's Compositor. Let's add the Blur effect. Open the Add menu by pressing Shift+A and select Filter → Blur from there.
- Drag the Blur node over the connection path and once it becomes white, make a single click.
- From the drop-down menu, select Fast Gaussian instead of Gaussian and choose your X and Y values for the blur size.
It should look something like this (except for the Backdrop which I have disabled):

- Switch back to the Video Editor layout and voilà! You can notice that the blur effect is much more responsive now.
- In order to animate the effects, you need to switch back to the Compositor and utilize the keyframing from there.
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