(CNN) House Judiciary Chairman Jerry Nadler is pushing to empower committee chairs to hold individuals in contempt of Congress without going to the floor for a full House vote, a move that could expedite Democrats' ability to punish anyone who defies their subpoenas but also risk further escalating tensions between congressional Democrats and the White House.

Nadler told his colleagues at a meeting Thursday that he's looking at the change as a way to avoid clogging up the floor with contempt citations in the face of near all-out resistance to Democratic subpoenas, according to a source in the room.

The New York Democrat also wants to hold a floor vote on a contempt package the week of June 4, House Majority Whip James Clyburn, a South Carolina Democrat, told CNN on Thursday. That would include a vote to hold Attorney General William Barr in contempt and possibly former White House counsel Don McGahn. Yet a number of Democrats are pushing to levy heavy fines on McGahn to warn future witnesses to comply with House subpoenas.

It's unclear whether House Speaker Nancy Pelosi, a California Democrat, will embrace this change to expedite contempt citations, since doing so could set a precedent for future House majorities to give more power to their chairmen at the expense of their leadership.

Nadler's committee has already voted to hold Barr in contempt. It has not yet done so with McGahn, but Nadler vowed to punish McGahn when he failed to testify under subpoena at a hearing this week after the White House directed him not to appear.

Read More