Can the Government Tax Itself?

Taxation;

It depends on who the taxing authority is.

If the taxing authority is the National Government as a rule YES.
Except GSIS, SSS, PhilHealth, PCSO (Sec. 27C) and income derived from the exercise of essential government function accruing to the Government of the Philippines or to any political subdivision (Sec32b7b NIRC)

If the taxing authority is the local government units, as a rule - NO.
LGU's are expressly prohibited from levying tax against
1.National Government
2. Its agencies and instrumentalities
3.Local Government Units.

Except: Sec. 154 of the Local Government Code states that LGU's may fix the rate for the operation of public utilities owned and maintained within their jurisdiction.