Dunleavy wants the state to issue $325 million in bonds to pay for construction on ports, airports, fire halls and other projects.
No direct deposits went out Monday because it was a federal holiday, said Genevieve Wojtusik, a spokesperson for the department.
Alaskans who filed electronically and chose direct deposit will receive their PFDs the week of Oct. 11.
Alaska lawmakers have been filling multibillion-dollar deficits with money from savings accounts. But those are now effectively depleted, making Permanent Fund earnings an increasingly attractive option to lawmakers.
As a special session begins in Juneau, momentum seems to have stalled amid disagreements over the size of the Permanent Fund dividend.
Alaskans have until 11:59 p.m. Alaska time on Wednesday, March 31, to submit their applications online.
Gov. Dunleavy has proposed putting PFDs in the state constitution, as part of an amendment that would outline rules for the overall annual draw from the fund.