We consider the excitation of atomic hydrogen in its ground state by an intense radiation field tuned close to the ionization threshold. Results are presented for the ac Stark shift of the 1s and 2s states, the width of the 1s state, and the photoelectron energy spectrum. In the first instance, our nonperturbative approach includes the 1s state, the p series of excited states, and the p continuum: we demonstrate that the p Rydberg states generate a rich structure in the photoelectron energy spectrum through the action of the counter-rotating wave dynamics when the laser frequency is tuned below the ionization threshold. We then go on to analyze in detail how the interaction of the p states with the other Rydberg series and continua increases the width of the p states; it is shown, however, that at the field intensities considered here (\ensuremath{\approxeq}
1013 W ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$), this effect is not sufficient to smear out the structure in the photoelectron energy spectrum.