You better get moving if you want her to have any chance of being assigned an SSN.
SSA will not assign an SSN or issue a card to an individual that is within 14 days of his or her alien status expiring. Until the 76th day after entry an individual with K-1 status only needs to provide an unexpired I-94 showing current K-1 status to establish employment authorized status for SSN purposes.
RM 00203.210 C. Procedure - Immigration Document as Evidence of Legal Name:
“When an alien applies for an SSN card, we presume the name on the immigration document is the legal name unless the applicant presents evidence of a legal name change, e.g., marriage, which occurred after the immigration document was issued.”
RM 00203.210 Changing Numident Name Data:
http://policy.ssa.gov/poms.nsf/lnx/0100203210Normally, an SSN card should be received in the mail within two weeks after the application and document(s) have been received and verified.
However, when an alien requests an SSN or replacement card, we must verify his or her documents/current status with the appropriate Bureau of the Department of Homeland Security. If the initial online verification is not possible through the Systematic Alien Verification for Entitlements (SAVE) system, we may need to send a Form G-845 to the appropriate Bureau of the Department of Homeland Security for manual verification.
Since 01/06/2007 Social Security field offices can submit an additional electronic online verification, which in the majority of applications eliminates the need to send a Form G-845 along with copies of the applicant’s immigration documents.
However, some applications still require a copy of the immigration document(s) being verified to be sent at the request of the Department of Homeland Security along with the Form G-845 for manual verification.
Note: If the applicant has changed his/her name after an immigration document, i.e. I-94, was issued, e.g., married and is now using the married name, but has not obtained a corrected immigration document showing the new name; this is not a name discrepancy for enumeration purposes, i.e. SAVE clearance, if the applicant can provide an acceptable legal name change document to establish the new name.
The 14 day status expiration limit for assigning an SSN and/or issuing a card applies even if an individual submitted his or her application before being within the 14 day period and entered the 14 day period while waiting for his or her status to be verified.