Nick Merrill, a spokesman for Mrs. Clinton, said of Priorities: “While they are an independent entity acting on their own, their enthusiasm is flattering. In the end though, only she can make that very personal decision, and as she has said, she won’t be doing so anytime soon.”

Mr. Messina is now the highest-profile member of Mr. Obama’s inner circle to openly back Mrs. Clinton for president, a move that can only fuel perceptions that Mrs. Clinton’s potential candidacy has the tacit endorsement of Mr. Obama himself.

Donors and others involved with Priorities said that they would look to far surpass the $67 million that Priorities spent on attack ads against Mitt Romney during the 2012 election. Those ads — including the “coffin ad,” featuring workers laid off from a plant acquired by Bain Capital, Mr. Romney’s former firm — helped define Mr. Romney early in the campaign, a blueprint the group hopes to use on Mrs. Clinton’s prospective Republican opponents.

Steve Mostyn, a prominent Houston trial lawyer and Democratic donor who, with his wife, Amber, was among the earliest major donors to Priorities in 2012, said he believed that liberal donors would come out in force if Mrs. Clinton enters the race.

“Amber and I are both excited about the prospects of being part of the super PAC for Hillary if she decides to run,” Mr. Mostyn said. “The first time was kind of a leap of faith for us — it was back when no one was giving Priorities money. I think it’ll be easier with Hillary.”

Mr. Messina said he would focus on importing to Priorities some of the advances in television microtargeting developed by the Obama campaign in 2012, which allowed it to achieve unusual precision and cost-efficiency in finding and reaching voters, out-hustling big-spending groups on the right.