By Specialized Sirrus, I'm assuming you mean the aluminum one with flat bars that first came out in the early 2000's. (Earlier Sirrus models were steel frame with drop bars.)
I commuted daily on one of the flat bar models for eight years and absolutely loved that bike as a commuter. I even thought it would make a decent tourer with its triple crank, triple water bottle mounts, mounts for rear and front low rider racks and ample space for fenders. For my commute, I never used tires wider than 28s, but there should be room to go wider.
That said, I also think there are some drawbacks for a tour on the scope of the TransAm. I don't believe the flat bars offer enough hand positions for a tour of that length, even with bar extensions. I also had issues with frequent spoke breakage on the rear wheel, even with a light commuting load. (I had the rear wheel rebuilt and that greatly reduced spoke breakage, but that was with loads far less than a cross continental journey would require.)
The bottom line is I would not generally recommend a Sirrus for a TransAm without some modifications. I believe you will experience more discomfort and equipment problems than if you were using a bike more dedicated to touring. However, you could do worse and people have probably completed such a trip with far less suitable bikes.