The congressional pushback against President Obama’s military operation in Libya entered a new phase Tuesday, as a Senate resolution supporting the White House appeared stalled and discussions on a separate, more critical, measure moved forward.

Lawmakers from both parties have grown increasingly restless since the Libya campaign began in mid-March. With the U.S. currently providing support for a NATO-led mission, members of both the House and Senate are divided over how hard to push the White House

Sens. James Webb (D-Va.) and Bob Corker (R-Tenn.) are working on a resolution that would chastise the administration for failing to consult with Congress. Though the details remain in flux, the measure could resemble one proposed by House Speaker John Boehner (R-Ohio) that passed the House by a wide margin last week, with 45 Democrats joining most Republicans in support.

Boehner’s bill, which would not have the force of law even if passed by the Senate, gave the White House 14 days to provide more information about the mission and prohibited the use of ground troops. Boehner’s resolution was designed to be a compromise, as the House rejected a bill by Rep. Dennis Kucinich (D-Ohio) that called for the U.S. to pull out of the Libya operation.

The White House was dismissive of the Boehner bill, and Sen. John Kerry (D-Mass.), the chairman of the Foreign Relations Committee, and John McCain (R-Ariz.) have proposed a separate resolution that would offer congressional support for the Libya campaign.

But a Foreign Relations hearing to consider the Kerry-McCain resolution that had been scheduled for Thursday has been postponed, amid questions over whether it had the votes to clear the committee.

Kerry spokesman Frederick Jones declined to comment on any efforts that might be underway to alter the measure. “Debate on the resolution will be taken up as soon as the business meeting is rescheduled,” he said.

Sen. Richard Lugar (Ind.), the top Republican on the Foreign Relations panel, wrote in a much-noticed Washington Post op-ed Monday that the White House should “understand the significance of [the House] vote, abandon its plans for a nonbinding resolution in the Senate and proceed to seek the requisite debate and authorization for the use of military force.”

A Lugar spokesman said Tuesday afternoon said the senator was waiting to see what alternative resolutions were offered before deciding what he would support.

Senate Majority Leader Harry Reid (D-Nev.) told reporters Tuesday he had spoken to both McCain and Kerry, “and I’ve told them that I am going to do my utmost, either through a bill that comes out of the Foreign Relations Committee or use some of the procedural avenues I have to bring something to the floor so we can have that debate.”

As for other measures, Reid said: “We’re going to have lots of opportunities to vote on different things on how people feel about Libya. So I don’t think it’s -- I’ll be happy to look at every different idea that people have, from [Sen.] Rand Paul [R-Ky.] to whoever else wants to bring something up.”

Webb, a former Navy secretary, has been outspoken in criticizing the administration’s approach to Libya. At a hearing last month, Webb said he was troubled by Obama’s use of the military in a situation where “we were not under attack, we were not under a threat of an attack, we were not implementing a treaty, we were not rescuing American citizens [and] we were not responding directly to an incident.”

Webb added that the decision “could set a very disturbing precedent for how decisions are made for the use of force.”

Staff writer Felicia Sonmez contributed to this report.