Eventually, even the most gleeful child learns that there is such a thing as too much ice cream when the carton is empty and all that’s left is the toothache. Might conservative Iowa Republicans, a demographic that plays an outsize role in the presidential nominating process, ever feel the same way about Ted Cruz?

The Texas senator has been in office for less than a year and has already become a national figure and a frontrunner not just in the 2016 Iowa caucuses but eventually to receive the GOP nomination as well. Indeed, according to prominent Iowa conservative leader Bob Vander Plaats, Cruz would win the Iowa caucuses “going away” if they were held today. His problem is that they still are two years away, plenty of time for even those conservatives most excited by Cruz to tire of the Texas senator.

Cruz’s 21-hour anti-Obamacare speech on the Senate floor on the eve of October’s government shutdown established him as a national figure, but his star had been rising before that. It was Cruz’s performance in the 2012 Texas Senate primary, when he won as an underdog Tea Party candidate, that gained him prominence in the Republican Party. Cruz combined Hispanic heritage (his father was born in Cuba) with unimpeachable conservative credentials and a sterling legal record as Texas’s solicitor general, arguing nine cases before the Supreme Court and drawing comparisons to a fellow Harvard Law graduate, Barack Obama.

The Obama comparisons ended once Cruz took office. As a junior senator, Cruz has aggressively courted national media coverage to promote his causes, a strategy counter to the one President Obama used when he first entered Congress. According to Tommy Vietor, a former Obama Senate press aide who later worked for Obama both on his 2008 campaign and in the White House, the then-Illinois senator “basically declined every national press interview for nine months once he took office.” It was the same approach taken by Hillary Clinton when she was elected in 2000: “Keep your head down, focus on your work, and don’t look like you’re a show horse.”

In Vietor’s opinion, “when you’re an elected official and out doing every possible interview and on cable news, it diminishes you and makes people wonder why you aren’t spending more time doing your actual job.” As senator, Obama also took pains to avoid the appearance of even considering a presidential campaign and only visited Iowa twice before beginning his presidential campaign, both times while campaigning for fellow Democrats in the runup to the 2006 midterm elections.

By contrast, some grassroots Iowa Republicans say Cruz has hit just the right notes. Jamie Johnson, a member of the Republican Party of Iowa’s state central committee, said Cruz’s approach to the Hawkeye State has been “just right.” He noted that the Texas senator has made three trips to Iowa, each for a high-profile event, and that he likely won’t be back in the Midwest until next spring. Craig Robinson, a former party operative and editor of the Iowa Republican, voiced a bit more skepticism. While he acknowledged that Cruz has been in the state “a lot,” his criticism is not so much that the Texas senator is spending too much time in Iowa but that he has been concentrating on the wrong parts of the state. Cruz has been “been Des Moines-focused,” Robinson said. “It would be a bigger deal to me if he went to Dubuque or Davenport. That would be more interesting, rather than repeating” his trips to metro Des Moines.

As a presidential hopeful on the right of the Republican Party, Cruz has far more reason to visit Iowa in an effort to attract publicity than most of his potential competitors. After all, the past two winners of the Iowa caucuses, Rick Santorum in 2012 and Mike Huckabee in 2008, might run in 2016, along with a number of other conservatives with strong links to the state, such as Sen. Rand Paul (R-KY) or Gov. Rick Perry (R-TX), another former presidential candidate. Cruz is appealing to a specific slice of Iowa caucusgoers, committed conservatives who are far more familiar with his competitors. As one observer pointed out, he has “more ground to make up.”

The risk for Cruz with Iowa voters is that campaigning aggressively at this stage in the election cycle would expose any political weaknesses far earlier than they might be otherwise. Doug Gross, who was the Republican nominee for governor in 2002 and is associated with the pro-business, establishment wing of the GOP, said the Texas senator is exposing his “feet of clay.” Gross said he thought Cruz performed poorly on his most recent visit to the state in October, when he spoke at the Republican Party of Iowa’s Ronald Reagan dinner in Des Moines. In Gross’s opinion, Cruz gave “a 45-minute self-indulgent rant” that hurt him with Iowa Republicans and “was better suited for D.C.” than a friendly part of the Midwest, where “neighbors know neighbors.”

Of course, as Cruz spokeswoman Catherine Frazier emphasized, his speaking schedule isn’t just about Iowa. “The senator accepts event invitations and schedules interviews that offer the best platform for him to share his priorities and make the argument for the policies he is pursuing in the interests of the Texans he represents,” she said. She noted that Cruz’s camp was “mindful” of the risk of overexposure but still “pleased that his message has been able to resonate largely through the work he has done in his role as a senator—in committee hearings, statements on the floor, etc. Of course, media interviews are a part of getting that message out, too.”

The problem for most politicians is that they are never “new” for long. They all eventually become known quantities. While Vietor pointed out that Cruz has “completely diluted his sort of freshness factor and everything he says is completely predictable,” that’s the case with almost every public figure who has stuck around in politics. The Texas senator was always going to lose his initial bloom after the wave of publicity surrounding his 21-hour speech and his leadership role during the government shutdown. The question now is whether Cruz and his team can deliver a message that resonates and maintain an appeal with Hawkeye State voters who no longer see him as the exciting new guy.