Updated

Republican Sen. Ted Cruz rallied conservatives to keep up the fight to unravel ObamaCare, ahead of a White House meeting where his colleagues were expected to dial back their demands for changes to the health law as part of a possible deal to end the partial government shutdown.

Cruz and his Tea Party-aligned colleagues spoke at the annual Values Voter Summit in Washington, D.C., Friday morning.

The Texas senator, who along with Sen. Mike Lee, R-Utah, helped drive the showdown with the White House over ObamaCare, joked that he'd be heading next to the meeting with his colleagues at the White House, and "if I'm never seen again, please send a search-and-rescue team."

But Cruz also delivered a stern message to conservatives, amid signs that the upcoming meeting could lead Senate GOP leaders to dial back their demands on ObamaCare.

"We're nearing the edge of a cliff," Cruz said, focusing his remarks almost exclusively on the health law. "What does it take to win this fight? It takes the men and women in this room."

Cruz also urged the House of Representatives to keep "standing strong."

Cruz and his allies had demanded that ObamaCare be defunded as part of any spending bill. Failure to reach an agreement with Democrats resulted in the partial government shutdown which started Oct. 1. Lawmakers are now grappling with both the spending debate and a looming Oct 17 deadline to raise the debt ceiling.

House Republicans pitched a plan to the White House Thursday night to approve a short-term debt-ceiling increase, but President Obama pushed back because it did not address the partial shutdown.

Senate Republicans are now crafting an alternate proposal that deals with both. It includes a provision dealing with ObamaCare, but is far short of what Cruz campaigned for -- and advocated with a 21-hour address on the Senate floor last month.

The emerging proposal comes from Sen. Susan Collins, R-Maine, and others. It would propose a six-month extension of government spending, a repeal of the health care law's medical device tax and greater flexibility for agencies to deal with across-the-board spending cuts in effect this year.

Sen. John McCain, R-Ariz., said the goal was ending the partial shutdown and raising the debt limit, but said, "We will not defund ObamaCare."

Cruz, decrying the health law as a "train wreck," claimed the American people remain "energized" around the goal of gutting the law. He claimed it is causing "enormous harm" to the economy -- though the administration says there's no hard evidence that the economy is being hurt by the roll-out.

Cruz was also interrupted more than a half-dozen times by protesters. To the delight of the audience, he repeatedly accused them of being Obama's "political operatives."

"How scared is the president?" Cruz asked, as another protester was escorted.

Where the budget and debt talks go from here is unclear. One reason Senate Republicans might step up with a new plan is because Senate Majority Leader Harry Reid seemed to dismiss a key detail of the proposal from House Speaker John Boehner.

Reid said negotiations before the government reopens -- a key part of Boehner's proposal -- were "not going to happen."

Reid has proposed extending the debt limit through 2014, which would boost the current $16.7 trillion debt limit by around $1 trillion. He has been planning for a test vote by Saturday on the measure, which has no other conditions, but Republicans may have enough votes to block it unless he agrees to changes.

The Associated Press contributed to this report.