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I'm not an expert in any way but Portugal and the US have a tax treaty that eliminates double taxation. If you're filing tax returns in the US and all income is US based then it won't be taxable in Portugal. There is an option to become a tax resident in Portugal but believe you'll find it won't be advantageous. 

Thanks very much for this Bob, that is the answer i was hoping for 

Treaty between Portugal and the US to avoid double taxation:

(Select country  "Estados Unidos da América)

PDF - page 21 of 26.

Article 20: pensions

Hello! Social Security benefits received from the US government may be subject to US taxation depending on your total income and other factors. Social Security benefits are generally included in your tax base and you may be required to file a US income tax return. In Portugal you may also be subject to taxation according to local tax laws. In this case, you may need to additionally declare your income and payments in Portugal.

Thank you for this Terry but I do believe, as others have posted here and I have verified, that the US has an agreement with the Portugal of no double tax; so I will pay the SS tax in the US.

There was an article, on line, that included the countries that have this kind of agreemnt with the US I will try to post that here tomorrow.

After all this, I do still intent to speak with a tax specialist (Portuguese?) to be certain.

Under the US / PT tax treaty, both countries are entitled to tax Social Security - effectively you pay the highest rate of the two.

@TonyJ1 but you/I pay one: either the US OR PT?