This can be done by invoking SFIT and SERROR with the keyword LIK on the command line.
Since a spectrum is only Poissonian before background is subtracted, it is necessary to work with raw data, and allow for any background contribution as part of the model. However the software has been written such that you can use a background-subtracted, exposure-corrected spectrum, as for chi-squared fitting. The programs will reconstruct the raw data from this by scaling by the effective exposure time (stored in the spectral file HEADER) and adding back the background. However the software needs to be given a file containing the background subtracted. The ROSAT reduction software is configured to make this easy for the user, XRTSUB will generate a background model file, and enter a "BGFILE" flag in the spectral dataset pointing to it. This is then automatically picked up by the software. If you don't have a background file, then you can either construct one (e.g. from raw source spectrum - background subtracted spectrum) and make it known to the system by running SBG, or you can proceed without a background file, in which case the background will be assumed to be negligible.
The one drawback with likelihood fitting is that one does not get a measure of the goodness of fit (the numerical value of the likelihood does not help). The best way to judge the fit at present is to plot it out with SPLOT. The chi-squared statistic may also be useful, but very low values of reduced chi-squared are obtained for extremely Poissonian data.