The IRS is not going to penalize you for not paying in to Social Security. There are others who do not pay in to SS, either, such as lots of teachers, etc. who pay in to Teachers Retirement instead. Just enter your W-2 as it appears.
If you owe thousands it is for some other reason. Perhaps you are not having enough federal tax withheld from your paychecks.
https://www.irs.gov/individuals/tax-withholding-estimator
https://www.irs.gov/pub/irs-pdf/fw4.pdf
**Disclaimer: Every effort has been made to offer the most correct information possible. The poster disclaims any legal responsibility for the accuracy of the information that is contained in this post.**