Muse does not implement "Responsive Layout" as defined by a hand coder (which means using one HTML file and one set of images for multiple layout variations that are driven from multiple CSS definitions usually triggered by media queries).
However, Muse does provide a few features for creating a web page design that responds to some degree to resizing of the browser window:
1) Browser Fill Images set to Scale to Fill or Scale to Fit (generally with the page fill and stroke set to none, so the browser fill is the background everywhere)
2) 100% Browser width objects (which can contain background images set to Scale to Fill, Scale to Fit, Center, etc. and which can include text frames)
3) Pinned items, which maintain a specific location offset from one or two edges of the browser window
You may want to look through the sites at the Muse Site-Of-The-Day to get a feel for the spectrum of webpage designs Muse is capable of.
Updated August 4, 2014:A few additions to the list of features that respond to resizing of the browser window:
4) Full screen slideshows
5) 100% width slideshow hero images
6) 100% width Adobe Edge Animate animations (.oam files)
7) Some third-party widgets <https://creative.adobe.com/addons?pp=MUSE>