With Democrats fighting to keep control of the Senate in the midterms, the emergence of the pro-Clinton super PAC Priorities USA could eat into donations that the party’s candidates need to win in November, some Democrats warn. A number of Democratic groups are soliciting donors for money, including super PACS devoted to House and Senate races along with traditional party fundraising committees.

Aware of the anxiety, Priorities officials are considering tailoring their requests so that donors would be asked to write their biggest checks after the midterm elections are over, people close to the super PAC said. For example, Priorities might ask a donor to pledge $1 million to the Clinton effort over the next few years, but write a check for only $100,000 this year, a person familiar with the discussion said.

“My goal is to not have donors honestly say, ‘I can’t send money to you, House and Senate [candidates], because I’m giving all this money to Priorities,’ ” a person close to the process said.