You can try... but she is required to have a WHTI-compliant form of identification. This would be a passport, an enhanced driver's license (most Canadian provinces do not have these, and those that do charge additional fees for them), or a trusted traveler card such as NEXUS (which takes special effort to get).
Does she have an expired passport? This, combined with the ID you mentioned, and she may be admitted. And unless there is a long drive to the border, there is little harm in trying. But there is a decent chance that she will be denied admittance into the United States. Ideally she should have applied for her passport some time ago, or paid for rush service.