[MaxMax]

Doesn't this imply that the President can issue orders to the Guard only if Congress approves?

An act of Congress is one method for authorization but the Constitution also
allows the President to call up any American forces in order for him to perform
his Duty compelled by his oath as POTUS to protect our country from attack,
or in this case, invasion.

The president can order the border closed at any time without any approval
under most circumstances, health and welfare being one, invasion another.
There are more but they're not relevant to what's happening.

[Leaning Right]

the Constitution also allows the President to call up any American forces in order for him to perform his Duty compelled by his oath as POTUS to protect our country from attack, or in this case, invasion.

I was unclear in my original question about who can call up the Guard. I wasn't trying to give Obama a pass, saying he didn't have the authority.

Rather, I wondered about this: Suppose Perry found the courage to call up the Texas National Guard, and sent them to the border. Could Obama then federalize the Texas NG, and order them away from the border?