House Republicans frustrated with the military operation in Libya are drawing up a bill that would revoke funding for drone strikes and other offensive operations there, GOP aides said Wednesday afternoon.

The proposal hadn’t been formally drafted on Wednesday afternoon and its details were still unclear. The idea for it emerged after a gathering of the House GOP, in which members said that Libya-related resolutions offered by party leaders did not offer a strong enough rebuke of President Obama.

In response, GOP aides said, they were considering replacing a resolution that had been announced just a day before by House Speaker John A. Boehner (R-Ohio). That one would have “directed” President Obama to withdraw any U.S. forces not involved in support operations such as intelligence-gathering, surveillance and refueling.

Instead, they said, a new resolution would strip funding for any activities that go beyond support for the NATO-led operation. That would mean cutting off money for strikes by unmanned U.S. drones, which have continued to hit targets in Libya.

“You can do resolutions until you’re blue in the face” but still be ignored by the White House, Rep. Tom Rooney (R-Fla.) said in an interview after the meeting. Instead, he said, many Republicans in the meeting said they wanted to strike at the operation’s funding: “Are we going to pull the trigger, and cut off the faucet?”

It was also unclear when the new resolution might come up for a vote: Aides said it could be Thursday or Friday.

The House has been feuding with Obama for weeks over the operation in Libya, now more than three months old. Legislators have said Obama has ignored the 1973 War Powers Resolution, which requires presidents to obtain congressional authorization after they send U.S. troops into hostilities abroad.

Obama’s reply was that the Libyan operation — in which U.S. forces play mainly a supporting role — does not meet the definition of “hostilities.” Therefore, he said, Congress’ permission isn’t needed.

If that was intended to defuse anger on Capitol Hill, it didn’t work.

On Thursday, the House was planning to hold two votes designed to rebuke Obama. One would be a resolution to authorize the Libyan campaign — along the lines of one proposed by Sens. John S. McCain (R-Ariz.) and John F. Kerry (D-Mass.) in the Senate.

In the House, that one is expected to fail.

Also on the table was a resolution that would “direct” the president to withdraw all U.S. forces not involved in support operations such as refueling, search and rescue, reconnaissance and intelligence-gathering. That would appear to leave out the unmanned U.S. drones that have carried out some attacks on the forces of Libyan leader Moammar Gaddafi.

Rooney said some legislators in the GOP meeting thought that that one didn’t go far enough.

“What happens if that resolution goes to the Senate, and they don’t pick it up?” Rooney said. He said the bill to defund some Libyan operations would send a stronger signal.

However, even if a bill to cut off funds was approved, it would have to pass the Senate — an unlikely prospect, with Democrats in control.