Q:

Do I need an ASV to come out when going for an SAQ?

Our company is going for a SAQ, under PCI DSS 3.1. 
Do we need to pay a vendor to come out and do an on site scan, or can we use something like Nessus to do the scan on our own?

A:

Only the external scan requires an ASV:
PCI 3.1 states:

11.2.2 Perform quarterly external vulnerability scans, via an Approved Scanning Vendor (ASV) approved by the Payment Card Industry Security
  Standards Council (PCI SSC). Perform rescans as needed, until passing
  scans are achieved.

It is only on internal scans where you can run a tool such as Nessus (em mine):

11.2.1 Perform quarterly internal vulnerability scans and rescans as needed, until all “high-risk” vulnerabilities (as identified in
  Requirement 6.1) are resolved. Scans must be performed by qualified
  personnel.
verify that the scan was performed by a qualified internal resource(s)
  or qualified external third party, and if applicable, organizational
  independence of the tester exists (not required to be a QSA or ASV)

The external test does not require anyone "coming out". You can simply use an automated service such as Hacker Guardian which will satisfy the scan being done by an ASV.

