These are the two relevant sections of the statute relating to payroll taxes (other than regular income taxes). No mention is given of any authority of the President to suspend said tax collection.
And this section is relevant to me as representative of my employer:
(3) Tax paid by recipient
If an employer, in violation of this chapter, fails to deduct and withhold the tax imposed by section 3101(b)(2) and thereafter the tax is paid by the employee, the tax so required to be deducted and withheld shall not be collected from the employer, but this paragraph shall in no case relieve the employer from liability for any penalties or additions to tax otherwise applicable in respect of such failure to deduct and withhold.
If I actually listened to Trump and failed to withhold taxes from my employees, my company could be subject to tax penalties.
Thus my memo ordering my payroll departments to continue to collect payroll tax (and income tax) as normal.