"If you get outside of Washington, D.C., there is a frustration with Washington that is palpable. When you ask your constituents what are the problems you're facing, over and over again, the answer that comes back is Obamacare is killing jobs, is taking away my health insurance, is driving up my premiums, is causing small businesses to shrink, to go out of business. If we listen to the American people, that should be our priorities," he told CNN this week.
Still, Republicans are frustrated by his insistence on fighting a divisive, losing battle.
"We are giving Obama the escape out," Republican strategist Ana Navarro said on CNN's "AC360." "Instead of now focusing on the problems with Obamacare, everybody's focused on the civil war in the Republican Party."
Navarro also noted the numerous polls, including CNN's latest poll, that said while citizens are concerned about Obamacare, they don't support shutting down the government over it.
"If you want to fix Obamacare or repeal it or fix it or change it, the best way to do it is to elect more Republicans. And the political cost of a government shutdown is really going to affect any -- any possibility of electing more Republicans," Navarro added.
Or political genius?
While Cruz is ruffling the feathers of his colleagues in Washington, he is mobilizing the grass roots outside the Beltway.
Conservative groups are praising him.
"Senator Cruz came to Washington to advance conservative policies, not play by the same old rules that have relegated conservatives, and their ideas, to the back bench," Michael Needham, president of Heritage Action, recently said about Cruz.
His group helps activate grass-roots Republicans for conservative candidates and political causes.
And Republican candidates running against Republican incumbents in the primaries are using Cruz's crusade in their races.
Matt Bevin, who is running for Senate to replace top Senate Republican Mitch McConnell, said in a statement that he would support "conservatives like Sen. Ted Cruz in his fight to defund Obamacare."
Bevin bashed McConnell for coming out against Cruz's effort to shut down the government in order to stop Obamacare.
Like so many other crucial fights, Mitch McConnell has caved to (Senate Majority Leader) Harry Reid on Obamacare and is refusing to fight to defund this disastrous legislation."
And longtime Sen. Mike Enzi of Wyoming came out in support of Cruz. He is facing Liz Cheney, the daughter of former Vice President Dick Cheney, in a contentious primary.
Will Cruz be scarred or be a star?
Cruz could alienate his colleagues to a point where he becomes marginalized and completely ineffective in Washington.
He has also hinted at a possible presidential run in 2016. If he has no Republican Party support, he risks being cut off from its financing and other resources.
On the other hand, Cruz's principled stand could help to grow a movement of disenchanted conservative voters. If a groundswell of conservative grass-roots activists grows between now and 2016 -- and their financial support grows, too -- Cruz could have carved out a path to the Republican nomination.
"I think what Senator Cruz understands is that he has more to gain from adhering to his principles, staying in touch with the grass roots here and around the country, than he does being friends with other senators," said Brendan Steinhauser, a leading Texas tea party activist who worked to get Cruz elected.