This news only states that it will affect the "right-to-carry" permit applications, but it sounds like it will also affect any first time firearms permit applicants as well.

The Federal Bureau of Investigation has notified state law enforcement agencies that all fingerprint-based background checks necessary for Right-to-Carry permit applications will be temporarily suspended from April 28, 2010, to May 3, 2010.  The temporary suspension is said to be necessary in order for the FBI to process almost 500,000 fingerprints for Census Bureau workers. 

The FBI will resume processing CHL applicant fingerprints beginning May 4, 2010.  Delays from the suspension of up to two weeks are anticipated; with the FBI giving assurances that all fingerprints will be processed as quickly as possible.

Interesting...HRS 134-2(e) says:  no permit shall be issued to an applicant earlier than fourteen calendar days after the date of the application; provided that a permit shall be issued or the application denied before the twentieth day from the date of application.

But I see no language about why a permit may be denied...so, at least by my reading, it is possible that a delay by the FBI may cause a permit to be denied.

Sounds to me like they are suspending the service, and not necessarily processing permits without fingerprint checks.