With Election Day now only a few weeks away, the race between incumbent Republican Texas Sen. Ted Cruz and U.S. Rep. Beto O'Rourke has attracted national and international attention.

For Cruz, a star in national conservative politics, losing to O'Rourke would be a particularly bitter pill. Cruz rose to prominence during the heyday of the Tea Party, and was the last man standing against Donald Trump in the 2016 Republican presidential primary. He’s being challenged by a magnetic candidate embraced by both Texas and national Democrats – and, it’s fair to say, an adoring press.

So can O'Rourke defeat Cruz?

We’ve conducted public opinion polls throughout Cruz’s electoral career as principals in the most frequent statewide political poll in Texas, the University of Texas/Texas Tribune Poll, and we’ve worked closely with statewide election data. Even if O'Rourke manages to increase Democratic turnout beyond reasonable expectations, it is very unlikely he can overcome the structural obstacles he faces in Cruz’s existing advantages.

O'Rourke’s challenge, by the numbers

One poll in the late summer found that 15 percent of likely Republican voters said that they’ll cast a vote for O'Rourke. Other polls have found the size of the pool of potential Republican defectors closer to 6 percent. We believe the 15 percent figure is likely an outlier, especially considering there’s little evidence that GOP voters in Texas have soured on President Donald Trump. The estimate of 6 percent is more consistent with the current level of partisan polarization in Texas and the rest of the country.

We can use these poll results to estimate potential 2018 vote shares based on turnout data from recent midterm elections.

The average number of Republican votes in gubernatorial and midterm Senate races in 2010 and 2014 has been about 2.8 million, according to records kept by the Texas Secretary of State. The average Democratic vote total in those races has been approximately 1.9 million. In other words, historical results suggest approximately 900,000 more Republican voters than Democratic voters in the average midterm election.

A hypothetical defection of 6 percent of Republican votes to O'Rourke subtracts about 168,000 votes from the average GOP vote total.

Even if we were to assume that all of these Republican voters fled to O'Rourke – as opposed to just staying home – that would leave Cruz ahead by approximately 564,000 votes. Could Democrats increase turnout enough to close that gap?

It would be an uphill battle, with hopes of victory resting on mobilizing groups with historically low turnout levels in midterm elections, such as young voters and Democratic-leaning Latinos. Exit polls for recent elections illustrate just how difficult this has been in recent history. Latinos, for example, made up only 17 percent of the electorate in 2014. In that year, nearly half of Latino voters backed the Republican candidate, and the Democrat lost by 20 percentage points.

But let’s imagine that O'Rourke manages to mobilize an additional 20 percent to the baseline Democratic vote – an optimistic estimate for O'Rourke. That would add another 380,000 votes to the Democrat’s total – still short of Cruz’s projected vote total by 184,000 votes.

Those numbers predict a closer race than usual – but one that Cruz still ends up winning.

Can Ted Cruz stay the course?

The task before Cruz is both simpler and easier to achieve.

Cruz needs to sustain historical levels of GOP turnout in order to absorb a potential uptick in Democratic turnout. This requires recognizing and combating both the possibilities of GOP defections to O’Rourke and of GOP voters declining to show up.

The recent salvo of Cruz ads and social media, as well as Cruz’s approach in the candidates’ first debate, have negatively portrayed O’Rourke’s progressive policy positions on issues like border security and racial justice as dangerously outside the mainstream. In their first debate, when a moderator asked the candidates to say something positive about each other, Cruz used the opportunity to praise O'Rourke for being passionate, energetic and sincere in his beliefs – while asserting that those beliefs were “socialism,” complete with a Bernie Sanders name check. Cruz’s critics attacked him for red-baiting, but the message was no doubt received loud and clear by Republicans watching the debate or reading the media coverage the following day.

While this may make Cruz seem like “a jerk,” to some, this approach is designed to mobilize the voters he needs to get re-elected. Expect to see a lot more of the same through Nov. 6.

Democrats and credulous reporters talk of blue waves – that is, a significant uptick in Democratic turnout. They see destiny in demographics, believing that the increase in the Latino share of the Texas population ensures a Democratic resurgence. However, we predict Cruz and other GOP incumbents will likely survive one more election cycle in Texas. If there is a whiff of desperation to Cruz’s strategy, it may be an indicator that the comfortable margins of victory assumed by Republicans for the last decade are eroding, albeit much more slowly, and less decisively, than Democrats hope.

The authors do not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and have disclosed no relevant affiliations beyond their academic appointment.