The show of support for Cruz's PAC is another sign that the men are becoming allies.
Obama has committed to doing at least six fundraising events for the committee this year.
The decision follows pressure from congressional Republicans to push the rule back.
Priebus said he would "absolutely" look to challenge caps on donations.
Alabama businessman Shaun McCutcheon hailed the ruling as a win for individual rights.
Members of the Federal Election Commissioners are lashing back at campaign finance decision.
Wednesday's campaign finance ruling was one of a string of cases showing Thomas's influence.
The White House denounced the Supreme Court's ruling, but it hasn't said what it will do.
Mike Lillis 04/03/14 01:47 PM EDT
"Is this just supposed to be a money war?" she asked.