Supporters are encouraged to pitch in at least $3 to win the all-expenses-paid trip.
The DSCC reported raising $3.77 million, compared to $3.3 million for NRSC.
"My brother will be a tremendous President," he wrote in a fundraising letter.
The conservative group is accepting donations for Bush, Walker, Cruz, Paul and Rubio.
The End Citizens United PAC has endorsed 11 Democrats so far.
Correct the Record and Priorities USA are creating a joint fundraising committee.
The haul for Security is Strength puts Graham near the bottom of the GOP field.
Super-PAC fundraising puts him in the mix with Walker, Rubio, Perry and Christie.
The majority of the haul came from just two donors.
The RNC ended the second quarter with $16.1 million in cash-on-hand.