Related to this question about single-stage-to-orbit vehicles, the Atlas-B launch vehicle seems to have been the closest to a true SSTO solution. Although it did jettison booster engines, the vehicle was basically a single stage -- often referred to as "stage-and-a-half" configuration.
Could the Atlas-B have made it to a relatively stable orbit without jettisoning those engines? Even if it carried no payload? Note that this Astronautix page provides some numbers we can use for analysis and simulation.
I welcome any modifications to this question in regards to what defines a "relatively stable orbit", but let's say we just want to reach an orbit that won't decay for at least 24 hours.