"...The relationship between nonprofits and government is a marriage that can't end in divorce. Government needs us to deliver our services, and we need government to scale our services to meet our mission. There's no way we can privately fundraise our way out of this..."
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'Scale' used here as a verb means to match the size of one thing in proportion to another. To my surprise I have not found this definition of this word after a short search; the nearest is as a noun:
the relation between the real size of something and its size on a map, model, or diagram:
which I found at Cambridge dictionary. The usage you quote is a noun-as-verb version of this definition. It's commonly used in this way in business jargon, and in computing as 'at scale' to mean that a system, especially a web-based one, will function with a high volume of users, and not just as a small demo or proof of concept.
The OED offers some help with the verb (trans) scale :
b. With down: To reduce in amount according to a fixed scale or standard. Also loosely, to reduce. Also Comb. scale-down attrib. ? orig. U.S.
c. With up: to increase in amount or size according to a fixed scale or standard; to increase from a small scale to a larger scale. Also absol.
The examples are not up to date :
1979 Daily Tel. 19 May 2/1 The original pay claim for a 30 per cent. rise has been scaled down to 16 per cent.
1979 Sci. Amer. Jan. 45/1 Several organizations are currently scaling up from laboratory-size cells to units of demonstration size.
d. To measure or represent (a quantity) in exact proportion to its absolute size or according to an arbitrary defined scale.
e. To alter (a quantity or property) by changing the units in which it is measured; to change the size of (a system or device) while keeping its parts in constant proportion.
I would say that the last highlighted definition is the most relevant, here.