Republicans have a strong chance of winning back the Senate thanks to the government shutdown fight provoked by conservatives, according to Sen. Ted Cruz Rafael (Ted) Edward CruzVideo of Lindsey Graham arguing against nominating a Supreme Court justice in an election year goes viral Sunday shows preview: Justice Ginsburg dies, sparking partisan battle over vacancy before election Democrat on Graham video urging people to 'use my words against me': 'Done' MORE (R-Texas).

Speaking at the Republican Leadership Conference on Saturday, Cruz said the demands from he and other Tea Party lawmakers is a key reason the GOP is in a good position, suggesting that party “graybeards” or the GOP establishment did not appreciate that fact.

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"They’re reaping the fruits of the battle, which is perfectly fine," Cruz said, according to The Washington Post. "But we need to take a moment to acknowledge the lesson of the battle.”

The two-week government shutdown from last fall was widely seen as a defeat for Republicans. GOP lawmakers refused to fund the government without including language that would defund ObamaCare, but ultimately agreed to reopen the government with effectively zero concessions. Polls at the time showed GOP popularity taking the biggest hit from the shutdown as the Republican Party was identified as shouldering most of the blame.

But the conservative firebrand said Saturday the fight placed a key spotlight on ObamaCare's problems. And as the landmark law saw a rocky rollout thanks to technical difficulties, the GOP was positioned well to capitalize on that, hopefully leading to electoral gains.

"Any wartime general will tell you that not every war is won in a single battle," Cruz said.

In his New Orleans remarks, Cruz continued to hammer on the healthcare reform law, as well as Common Core education standards, and efforts to enact new gun control laws.

“In Texas and Louisiana we define gun control real simple,” he said, according to McClatchy. “Hit what you aim at.”