Spencer Zwick is urging GOP businessman Alex Dunn to challenge Sen. Mike Lee (R-Utah).
Joe Heck, an Iraq veteran, is under pressure from national Republicans to get in the race.
Toomey outraised his likely Democratic opponent by $1.8 million in the first quarter.
He's the latest Republican to pass on the open Senate race.
Senate Democrats need to pick up five seats to regain a majority.
The NRSC brought in $10.9 million for the first quarter of 2015.
The Democrat announced he will stay in the Senate.
The GOP senator donated to every member of his congressional delegation except Rep. Salmon.
It's the latest sign the free-market Tea Party group intends to be a major player this cycle.
State Republicans say Will Weatherford would have been a formidable challenger.