Sen. Ted Cruz walked on stage to great fanfare Friday at the Values Voter Summit, an annual conservative gathering in Washington.

But not long into the Texas Republican's speech, hecklers tried to get under the senator's skin.

Cruz, however, largely remained cool--and roused his supporters even more when he stood up to the hecklers' jeering.

"I wish you would participate in the democratic process through speaking respectfully," he said to one of the protesters, as the audience applauded. "It seems that President Obama's paid political operatives are out in force today. And you know why? Because the men and women in this room scare the living daylights out of them."

At least some of the hecklers, who stood up one by one before being escorted out, were from the group Fair Immigration Reform Movement.

But Cruz, a potential presidential contender, quickly accused the demonstrators of being puppets for the Obama administration.

"I'm curious, is anybody left in the Organizing for America headquarters? I'm actually glad that the president's whole political staff is here instead of actually doing mischief in the country," he said.

After continued interruptions, he made an offer.

"I would welcome the president, if he wants to get a 100 of his most rabid political operatives in a room, I will answer their questions on television as long as he likes," he said. "And in exchange, all I would ask, Mr. President, is you take not a hundred but 10 men and women in this room and spend 30 minutes answering their questions for the American people."

When he wasn't combating hecklers, Cruz applauded his own efforts in leading the strategy to try and defund Obamacare through a must-pass spending bill. The Republican-led House followed his rallying cry and attached such measures to multiple spending bills, but the Democratic-controlled Senate refused to pass them--actions that ultimately led to the ongoing government shutdown.

"It is because of you that the House of Representatives has been standing strong because the House has been listening to the people," he told the audience.

On Friday he heads to the White House with other Senate Republicans to talk about the shutdown and looming deadline to raise the debt ceiling.

"So after leaving here I am going to be going to the White House. I will make a request: If I am never seen again please send a search and rescue team. I very much hope tomorrow morning I don't wake up amidst the Syrian rebels," he said.

CNN's Peter Hamby contributed to this report.