We study ionic microgel suspensions composed of swollen particles for various single-particle stiffnesses. We measure the osmotic pressure π of these suspensions and show that it is dominated by the contribution of free ions in solution. As this ionic osmotic pressure depends on the volume fraction of the suspension φ, we can determine φ from π, even at volume fractions so high that the microgel particles are compressed. We find that the width of the fluid-solid phase coexistence, measured using φ, is larger than its hard-sphere value for the stiffer microgels that we study and progressively decreases for softer microgels. For sufficiently soft microgels, the suspensions are fluidlike, irrespective of volume fraction. By calculating the dependence on φ of the mean volume of a microgel particle, we show that the behavior of the phase-coexistence width correlates with whether or not the microgel particles are compressed at the volume fractions corresponding to fluid-solid phase coexistence.