It is her job as governor to try to get as much money from the federal government.
As a president it is his job to pass the requests to congress.
The two roles are mutually exclusive, unless you are working for MSNBC.
I don't see anything in the Alaska constitution that says the governor has the duty to run to the federal government with hat in hand asking for a handout:
Section 3.16 - Governor's Authority.
The governor shall be responsible for the faithful execution of the laws. He may, by appropriate court action or proceeding brought in the name of the State, enforce compliance with any constitutional or legislative mandate, or restrain violation of any constitutional or legislative power, duty, or right by any officer, department, or agency of the State or any of its political subdivisions. This authority shall not be construed to authorize any action or proceeding against the legislature.
Section 3.17 - Convening Legislature.
Whenever the governor considers it in the public interest, he may convene the legislature, either house, or the two houses in joint session.
Section 3.18 - Messages to Legislature.
The governor shall, at the beginning of each session, and may at other times, give the legislature information concerning the affairs of the State and recommend the measures he considers necessary.
Section 3.19 - Military Authority.
The governor is commander-in-chief of the armed forces of the State. He may call out these forces to execute the laws, suppress or prevent insurrection or lawless violence, or repel invasion. The governor, as provided by law, shall appoint all general and flag officers of the armed forces of the State, subject to confirmation by a majority of the members of the legislature in joint session. He shall appoint and commission all other officers.
Section 3.20 - Martial Law.
The governor may proclaim martial law when the public safety requires it in case of rebellion or actual or imminent invasion. Martial law shall not continue for longer than twenty days without the approval of a majority of the members of the legislature in joint session.
Section 3.21 - Executive Clemency.
Subject to procedure prescribed by law, the governor may grant pardons, commutations, and reprieves, and may suspend and remit fines and forfeitures. This power shall not extend to impeachment. A parole system shall be provided by law.
Section 3.22 - Executive Branch.
All executive and administrative offices, departments, and agencies of the state government and their respective functions, powers, and duties shall be allocated by law among and within not more than twenty principal departments, so as to group them as far as practicable according to major purposes. Regulatory, quasi-judicial, and temporary agencies may be established by law and need not be allocated within a principal department.
Section 3.23 - Reorganization.
The governor may make changes in the organization of the executive branch or in the assignment of functions among its units which he considers necessary for efficient administration. Where these changes require the force of law, they shall be set forth in executive orders. The legislature shall have sixty days of a regular session, or a full session if of shorter duration, to disapprove these executive orders. Unless disapproved by resolution concurred in by a majority of the members in joint session, these orders become effective at a date thereafter to be designated by the governor.
Section 3.24 - Supervision.
Each principal department shall be under the supervision of the governor.
Section 3.25 - Department Heads.
The head of each principal department shall be a single executive unless otherwise provided by law. He shall be appointed by the governor, subject to confirmation by a majority of the members of the legislature in joint session, and shall serve at the pleasure of the governor, except as otherwise provided in this article with respect to the secretary of state. The heads of all principal departments shall be citizens of the United States.
Section 3.26 - Boards and Commissions.
When a board or commission is at the head of a principal department or a regulatory or quasi-judicial agency, its members shall be appointed by the governor, subject to confirmation by a majority of the members of the legislature in joint session, and may be removed as provided by law. They shall be citizens of the United States. The board or commission may appoint a principal executive officer when authorized by law, but the appointment shall be subject to the approval of the governor.
Section 3.27 - Recess Appointments.
The governor may make appointments to fill vacancies occurring during a recess of the legislature, in offices requiring confirmation by the legislature. The duration of such appointments shall be prescribed by law.
http://www.legis.state.ak.us/cgi-bin/folioisa.dll/acontxt/query=*/doc/%7Bt51%7D?