Thom Tillis's win Tuesday in North Carolina's Republican primary for U.S. Senate was unquestionably a major victory for the Republican establishment. What's also unquestionable is that it was only the first in a string of big tests the establishment will face during the next eight weeks.

Thom Tillis speaks to supporters at a election night rally in Charlotte, N.C., after winning the Republican nomination for the U.S. Senate . (AP Photo/Chuck Burton)

The outcome of those tests could either hamper or help the GOP's position headed into the fall midterms, in which they are chasing the Senate majority.

Tillis's nomination was a testament to three factors: A flurry of outside spending on his behalf; ads from allies that were not too confrontational; and a weak field of opponents who tried to wear the tea party label but never convinced powerful tea party interests to join them.

In upcoming primaries in Georgia, Idaho, Kentucky and Mississippi, some but not all of these elements will define the landscape, presenting the establishment wing -- which prizes electability above all -- with new challenges.

First, let's look at how Tillis did it. Outside groups rushed to his defense in the closing stage of his race. A cavalry of allies including American Crossroads and the Chamber of Commerce spent nearly $2.5 million boosting him across the finish line.

They mostly avoided getting too nasty against the intraparty competition, focusing their TV ads on Tillis's message and opposing Sen. Kay Hagan (D-N.C.). In doing so, they avoided ginning up anti-establishment fervor among the conservative base. That base often accuses Republicans in elected office or those who work in tandem with them of trying to bully tea party underdogs who run as outsiders.

It certainly helped Tillis that his opponents were weak and got no help from the Club for Growth or Senate Conservatives Fund, two groups that spend big money influencing primaries. The candidate who finished second to Tillis had to defend himself against cries of plagiarism. Enough said.

During the next phase of primaries the establishment is eyeing because they impact the battle for the Senate majority, the situation is more complicated.

The first two come on May 20 in Georgia and Kentucky. In the latter, Senate Minority Leader Mitch McConnell (R) has a comfortable advantage over businessman Matt Bevin and is expected to advance. Like most of the North Carolina tea party field, Bevin has fizzled.

But in Georgia, the situation is murkier because a runoff is all but certain. Rep. Jack Kingston and businessman David Perdue have appeared to move to the GOP forefront -- which would be good news for Republicans with prioritizing electability. Former secretary of state Karen Handel is also showing signs of life. But Reps. Phil Gingrey and Paul Broun -- who make Republicans most nervous -- could still play the role of spoiler.

Adding to the GOP urgency: Georgia and Kentucky also happen to be the Democrats' two best pickup opportunities. In both races, Democrats have fielded women candidates who are exceptional fundraisers.

While it does not factor into the path to the House or Senate majority, another May 20 primary will also test the establishment's muscle. Attorney Bryan Smith (R) is trying to unseat Rep. Mike Simpson (R) in Idaho's 2nd district. The U.S. Chamber of Commerce, which backed Tillis and just released a new wave of ads across the country, has been helping Simpson. The Club has been helping Smith.

From there, a June 3 primary in Mississippi is the next marquee showdown. State Sen. Chris McDaniel (R) has the backing of the Club and the Senate Conservatives Fund in his bid to unseat Sen. Thad Cochran (R). But unlike the senators who were felled during the past two cycles in primaries, Cochran and his allies hit the ground running against McDaniel. A super PAC supporting Cochran has been bludgeoning McDaniel on the air. Questions about controversial statements McDaniel made in the past have set the challenger back, too. But since he has the backing of powerful outside groups, McDaniel should not be counted out.

As we noted over the weekend, the tea party's best hope for notching an early win comes next Tuesday in Nebraska. The open U.S. Senate primary does not factor into the majority at all, since whoever the GOP nominates will likely win in November. But it has some interesting battle lines. The candidate backed by Sens. Ted Cruz (R-Tex.), Mike Lee (R-Utah) and Sarah Palin, not to mention the Club and Senate Conservatives Fund, is Ben Sasse, the president of Midland University. Sasse has been surging in recent weeks.

The establishment prefers former state treasurer Shane Osborn, who has faded. The wildcard is wealthy bank executive Sid Dinsdale, who is a lone wolf. If he wins, it will be a big blow to Sasse's national tea party allies, who went all in for him.

Tillis's win is a good first step for the GOP establishment in 2014. But it's hardly a conclusive one. The next eight weeks will tell us a lot more.