If I invest 6000 in a Roth IRA, does that give me a tax break

No. Only a traditional IRA can be deductible.  But a ROTH grows tax free so when you eventually take it out it comes out tax free including the interest.  

A Traditional IRA you get a tax deduction now and pay tax on all the distributions.

A Roth IRA contribution might qualify for the Retirement Savings Contributions Credit, a tax credit that can reduce your income tax liability, the same as would a traditional IRA contribution.  But as VolvoGirl said, other then the possible tax credit I've mentioned there is no immediate tax savings for making a Roth IRA contribution.  The main benefits of a Roth IRA contribution is the tax-free growth, provided the holding requirements are met and tax- and penalty-free distributions of your original contributions at any time.  For many people the long-term benefit of tax-free growth will be greater than the immediate tax deferral of a deductible traditional IRA contribution.