How much slower are big tires?
There is plenty of discussions on the internet about larger volume tires actually being faster than narrower tires.  For example, a recent Cycling Tips pod cast has a good discussion. However, real world experience will likely be the opposite due to the tire construction used on the majority of tires available in the market place. 

Tire construction

Unfortunately, tire construction is a confounding factor when discussing performance of large volume tires.  Most larger volume tires on the market use heavier casings and thicker tread, as they intended use case is "heavy duty".  Add in some puncture resistance strips (standard on most large volume tires currently in the market) and you get a very thick and stiff tire. 

A stiff tire will have higher rolling resistance compared to a more supple tire  due to a a process called hysteresis, where the energy required to flex the tire slows you down and higher suspension losses (which has also been termed impedance).  Suspension losses vary by road surface and can be quite high on rougher surfaces. Here a stiffer tire response more slowly to road imperfection (i.e., flexes to accommodate the imperfection), which in turn vibrates the rider. The vibrating soft tissue "consumes" energy (actually it converts forward momentum into heat due to internal friction within the body). BQ showed this in an extreme context, where very rough surfaces more than doubled the amount of effort required.   

All things being equal, a larger volume tire will also be heavier than a narrower tire.  Add in heavy duty construction found on most high volume tires, and you end up with a much heavier tire.  This results in a large weight penalty which can noticeably affect acceleration, furthering the feel of the tire being slower.

Because most high volume tires on the market have stiff heavy duty construction, these tires will typically have much higher rolling resistance than more narrow tires, which, on average, tend to be more performance focused, featuring more supple construction and lighter weights.  

Light Supple High Volume Tires

An exception to this generalization is light supple high volume tires, which are currently quite hard to find.  These tires will also have low hysteresis and very low suspension losses as the supple construction means the flex easily and the large volume means you can run them at a lower pressure, there by greatly reducing suspension losses.  On most real world road surfaces (especially open chip seal or gravel roads), these type of tires will be faster, than a narrower tire of similar construction due to the large difference in suspension losses. 

These typically will not have puncture protection, further adding to the suppleness. Lack of puncture protection is less of an issue in large volume supple tires, because the force placed on encountered objects by the tire is reduced due to the fact the tires flex easily and the tires are run at a lower pressure. This means the regular tire rubber is typically strong enough to resist the object and an extra puncture strip is not required.

Finally, a light suppler large volume tire will still be heavier than an narrower tire so there is an acceleration penalty. That said, this penalty is much smaller than with the "heavy duty" large volume tires and for most everyday riding it will be hard to notice.  It is therefore a bit of a non issue relative to the gains in comfort and higher sustained speed due to reduced suspension losses.

The real problem is getting your hands on light, supple, large volume tires.  Only a few brands currently exist, with pretty much all of them are being manufactured by Panaracer.