if me and and my file TAX return together. I work and she gets SS
If I don't pay tax does the IRS come behind her?

If you filed a joint return (Married Filing Jointly) you would both be fully responsible for any tax liability. It sounds like you (or I should say you wife) would be better off filing Married Filing Separate. This way your wife would not be responsible if you owe taxes. However you lose some tax advantages by filing married filing separate (example you would lose the ability to claim the EIC earned income credit).