Western lawmakers have pushed for expansion of the airport's so-called perimeter rule of 1,250 miles. If eased, the airport could see for the first time nonstop flights to cities such as Los Angeles, San Francisco, Salt Lake City and Phoenix.
Rockefeller said last week he had hoped to have a bill ready before the August recess but a final has yet to emerge.
The House is leaving town at the end of this week for the August recess.
The Senate passed a two-year $34.5 billion measure in March while the House passed a $70 billion bill that covers 2009-2012 last year.