On Friday, Sen. Ted Cruz (R-Tx.) headlined Iowa’s annual GOP fundraising dinner, speaking for 45 minutes without a teleprompter or notes. It was Cruz’s third trip to Iowa, likely in preparation for a 2016 presidential run.

Much of his speech was centered on Obamacare and the government shutdown, which he still believes was a success despite receiving no concessions from President Obama and angering many people in his party.

“One of the things we accomplished in the fight over Obamacare,” he said. “is we elevated the national debate over what a disaster, what a train wreck, how much Obamacare is hurting millions of Americans across this country.”

That’s not actually true. The shutdown overshadowed the launch of the government exchanges, which have had massive issues during the first couple of weeks and have seen only marginal improvements since. Once the shutdown finished and debt ceiling deal was complete, the media’s attention turned to Obamacare and the administration has been on the defensive since. Cruz’s strategy provided a distraction from Obamacare during what may be its darkest hour. That’s not exactly elevating “the national debate over what a disaster” it is. In fact, it’s the opposite.

But Cruz is right about one thing: the grassroots support around the country is impacting American politics.

“For everyone who talks about wanting to win elections in 2014 — particularly an off-year, nonpresidential year — nothing, nothing, nothing,nothing matters more than an energized and active and vocal grassroots America,” he said. “I’m convinced we’re facing a new paradigm in politics. It is the rise of the grassroots.”

At the fundraiser, Cruz pointed out five issues that the Tea Party base has successfully influenced:

1. Gun control and the Manchin-Toomey Bill
2. Sen. Rand Paul’s (R-Ky.) filibuster over drone policy
3. Comprehensive immigration reform
4. Bipartisan disagreement over Obama’s Syria strategy
5. The government shutdown

Looking at each one of those issues, it’s clear that Cruz has a point. Despite most Americans being in favor of universal background checks, pressure from the small but powerful gun-rights groups (most of whom are Tea Partiers) convinced lawmakers to oppose it. Paul’s filibuster made national headlines and provoked a new conversation over America’s drone policy. Immigration reform is also favored by the majority of Americans, including citizenship for the 11 million undocumented immigrants currently residing in the United States, but the odds of any legislation passing look slim thanks to the Tea Party. Obama’s decision to ask Congress for approval to attack Syria may not have resulted from grassroots anger, but the slim chances he had of receiving a force authorization were certainly a result of bipartisan opposition to his proposals. Finally, the government shutdown was the direct result of the Tea Party’s fury at Obamacare, forcing GOP lawmakers to go along or be labeled a RINO.

In each situation, the grassroots Tea Party base, despite representing less than a quarter of the electorate, had a significant impact on the policy debate. The Tea Party has earned this power by developing a vocal, angry foundation that it can mobilize to have an outsized effect on elections. Cruz is right. The grassroots truly is powerful.

However, what the junior senator has not grasped is that there is a limit to this power. In the end, the Tea Party still represents a small part of the electorate and their scorched-earth tactics have earned the derision of much of the nation. The problem with having enough power to block popular legislation is that you make a number of enemies by doing so. Cruz & Co. make even more enemies when they choose tactics that have no chance of success.

In the other four issues he cites, the conservative base achieved their goals. They scuttled universal background checks, immigration reform and a strike on Syria and brought drone policy to national attention. The government shutdown was different. It was bound to fail from the beginning, but Cruz didn’t care. Now, the Republican Party has its lowest favorability ratings of all time and Cruz’s favorables with non-Tea Partiers have plummeted. He’s solidified his position as cult hero amongst the Tea Party, but at the expense of alienating the Republican establishment, crowding out media coverage of HealthCare.gov’s struggles and damaging his credibility as a strategic thinker. Cruz is right that the grassroots has become a powerful force in politics, but the government shutdown revealed the limits of that power. Likewise, Cruz has become an imposing figure in the Senate, but the past month demonstrated that he faces limitations as well.