Doug, Absolutely yes, the are long-term potential problems with these steps remaining damp; this will destroy the adhesion of the mortar, and if your area is subject to ice & snow it can also cause the brick to shatter as water trapped in the brick freezes.
The water could be seeping in to the internal structure of the brick/mortar at joints to concrete, such as at the top step where it might meet the porch foundation, but it's also likely that the entire brick/mortar area is absorbing water; the steps should be sealed.
One ideal product for this is called Professional Water Seal, available from ICI Glidden. It is a liquified silicone product which can be applied with a pump-up garden sprayer.
It does not leave a surface coating, rather it absorbs into the surface and seals it off. On concrete, it is invisible and causes no color change; with brick I might expect a slight enhancement of the brick color, but not noteably. Basically you'll not even know it is there until it rains; this is when you notice that water on the brick will bead up and run off, rather than being absorbed. This is a one-time application, which does not require re-treatment yearly like many deck sealers do, and would be an excellent product for this application.
Should you find any small gaps where the steps meet the porch, I'd also close these off with a flexible mortar patch or polyurethane caulking, both available in a "mortar" color.