Yes, apply for the EFTPS as a business to pay the FICA/Medicare taxes for both of you. You will then report the share of the FICA/Medicare taxes on each of your W2's that was paid out by the partnership.
I am not sure what you mean by one of the partners paying. This should be paid from the income generated by the partnership so in a sense the partnership is paying the FICA taxes for both of you.. Let me know if you have a different interpretation.
Now if you have estimated income tax payments that are generated by not having enough income tax withheld on each W2, each of you may apply to EFTPS as individuals to make quarterly income tax payments on that income.
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