Another concern is the costs of DAFs. Financial institutions have piled into the market to gather assets and charge fees to manage them, and the costs vary widely across the industry. There are typically two fees: one for administration of the account and another for investment management of the funds.
The National Philanthropic Trust has an .85 percent (85 basis point) administrative fee. Depending on how active you want to be in the management of the account, the investment management fee can range from as little as the 10 basis points Vanguard Charitable pays annually to Vanguard to manage its roughly $4.6 billion in assets, up to 1 percent or more.
Proponents of the funds say DAFs are getting unfairly targeted. Sure, financial institutions have piled into the market to gather assets and charge fees to manage them, but private foundations pay advisers to manage assets as well. What's more, the payout ratios from DAFs as a whole are nearly 20 percent. That's about four times higher than the average payout of private foundations across the country and very close Camp's proposed five-year payout requirement.
Read MoreAre you giving too much to charity?
If people are worried about stagnant philanthropic structures, foundations may be the better target. They hold more than $600 billion in assets and on average pay out not much more than their 5 percent minimum annually.
"I think [DAFs] are a positive overall," said Keith Curtis, a consultant to nonprofit organizations and current chair of the board of the Giving USA Foundation. "They're introducing more people to philanthropy and helping them see what their gifts can do. That's a big benefit."
Curtis expects the growth of DAFs will moderate if the stock market cools off, but he believes their popularity will continue. "There's a lot of interest in these funds, and I hope they'll get people to think more philanthropically and do more for nonprofits," he said.