Indeed, if the federal training mission were to interfere with the State Guard's capacity to respond to local emergencies, the Montgomery Amendment would permit the Governor to veto the proposed mission.

Perpich v. Department of Defense, 396 U.S. at 351. (1990) (emphasis mine).

See also, Footnote #24:

The Montgomery Amendment deprives the Governors of the power to veto participation in a National Guard of the United States training mission on the basis of any objection to "the location, purpose, type, or schedule of such active duty." 10 U.S.C. 672(f). Governors may withhold their consent on other grounds. The Governor and the United States agree that if the federalization of the Guard would interfere with the State Guard's ability to address a local emergency, that circumstance would be a valid basis for a gubernatorial veto. Brief for Petitioners 41; Brief for Respondents 9. (emphasis mine).