Just make sure the cyclocross bike has a rear dropout spacing that matches your wheels which should be about 130mm rear spacing and obvious has the same diameter 700c, I'm assuming. Some bikes like the Surly Crosscheck is set at 132.5 so you can use either 130 or 135 no problem. If the new cyclocross bike have a 135 spacing. You can add spacers to your old 130mm rear wheel, no problem, but you don't want to go the other way around because your rear wheel will be severely dished making it weaker.

Cyclocross will be a tad slower and you'll get more of a workout, maybe add about 10-15 mins to the commute. Really depends on your fitness level and what kind of tires you will be running and how much psi are in them. I'm assuming the cyclocross bike will be a little heavier than your road bike, but there's some tricked out cyclocross bike out there so maybe you'll even go faster if you get a really light one.

I would not get anything bigger than 700 x 32. Too much rotational weight means more effort and a slower ride especially starting up from stop signs/lights.

700 x 28-30 is the sweet spot in terms of comfort, being safe from most potholes, cracks, sand, and speed.

Another thing, cyclocross bike are generally geared lower than normal road bikes so you might have to switch chainrings/cranks to get the fastest most efficient gear ratios for your commute.