You can buy a longer seat post to get your saddle up high enough ($25). you can also change the handlebars to drops ($30), but you may also need to replace brakes ($25) and/or shifters ($65) as well. Since that looks like a quill stem you might also be able to raise the handlebars as well. I know SixtyFiver has a rigid MTB with drop bars.

My Specialized FatBoys are 26*1.25 up to 100 psi. Nashbar slicks are also 1.25" ($20).

So probably a rough estimate of $165 if you do change everything. If you have parts lying around and shop around you can probably do it for cheaper.