Federal troops can't "police" anything. Rescue, provide comms, provide certain kinds of imagery, yup. Police work, nope.
AFAIK, there is no date where Blanco "let federal troops into the state." She managed the use of NG since before the storm (see Superdome screening), and other than active military evacuation activity, she was the top of the chain of command.
I think (but don't know for sure) that Gretna was indeed an exit corridor. But the Gretna Sheriff was concerned that people would not just "pass through," and the town could not police a significant increase in population. So, the rational reaction is to close the doors leading in, so population would not increase. Blanco could have provided resources to "enforce the corridor" - use the road but don't stay - but she didn't.