Originally Published: 01 MAR 22 16:50 ET

Updated: 02 MAR 22 14:24 ET

By Gregory Krieg and Maeve Reston, CNN

(CNN) -- Texas Republicans will need a May runoff to decide their nominee for state attorney general after incumbent Ken Paxton fell short of clinching a majority in Tuesday's primary, setting up a showdown with Texas Land Commissioner George P. Bush in May, CNN projects.

Paxton led the four-candidate field by a comfortable margin, despite feisty and well-funded challenges from Bush, former state Supreme Court Justice Eva Guzman and Rep. Louie Gohmert.

"I guess what I'd say is, clearly, to the establishment: they got what they wanted," Paxton said in a speech to supporters late Tuesday. "They got me in a runoff."

Texas Gov. Greg Abbott, a two-term incumbent, will defeat a crowded field of GOP challengers to secure the gubernatorial nomination, while Beto O'Rourke, a former congressman and Senate and presidential candidate, will win the Democratic nomination, CNN projects.

Votes are being counted in Texas in the first primaries of the 2022 midterms, with contests on both sides of the aisle poised to set the landscape for elections in November that could swing control of Congress to Republicans.

But as the results came in, Texas shared the spotlight with President Joe Biden's State of the Union address on Capitol Hill and the rapidly escalating crisis in Ukraine, where invading forces from Russia are moving in on major cities across the country.

Russian President Vladimir Putin's troops were camped out on the Ukrainian border when early voting began in Texas on February 14, and while the conflict appears unlikely to influence Tuesday night's elections, quick-moving events at home and abroad underscore the challenges facing candidates as the 2022 midterms begin in earnest.

The banner contest on Tuesday revolved around Paxton, the two-term incumbent who filed a failed lawsuit seeking to effectively overturn the 2020 election and ran under a cloud of legal issues, with the possibility of more on the horizon. His GOP challengers, led by Bush and Guzman, argued he could endanger the GOP's effort to yet again sweep statewide offices.

Polling ahead of Election Day showed Paxton with a commanding lead but suggested he would fall short of the majority he needed to win the nomination outright.

Bush, the latest in a political dynasty that, even with the Republican Party now in thrall to former President Donald Trump, maintains a considerable stature in Texas political circles and this campaign amounted a referendum on the future of that dynasty.

Like Bush, Guzman, who spent more than a decade on the state's high court, is a relative moderate. The pair clashed in a recent debate, which saw Guzman question Bush's qualifications and Bush denounce Guzman as a "gutter politician." More troubling for Paxton, though, was been the candidacy of Gohmert, whose ideological and geographic base overlaps with Paxton's.

The Democratic primary for attorney general will also go to a runoff, CNN projected.

Hanging over the primary were concerns -- at least among Democrats and voting rights advocates -- about the effect of the state's restrictive new voting rules.

Texas was the first of a number of Republican-led states to hold major elections after passing legislation, on the back of a political wave set off by Trump's long campaign to sow doubt over his loss in 2020, that complicates mail-in voting and outlaws other efforts to make the ballot more accessible. Some larger Texas counties have reported spikes in ballot rejections because would-be voters did not meet beefed-up and, to many, confusing new identification requirements.

As polls closed, Harris County officials warned of delays in reporting results, due to "damaged ballot sheets that need to be duplicated," according to a press release issued late Tuesday.

The primaries brought some poll worker shortages and other glitches, but Election Day itself was mostly calm -- with the scramble to fix the unusually high number of faulty mail-in ballots emerging as the biggest challenge from this first round of voting.

The leading problem, said Isabel Longoria, who presides over elections in populous Harris County, was voters did not include identifying numbers on the return ballot envelopes under the flap. The tally of potential ballot rejections as of Monday would represent 30% of the mail-in-ballots submitted in the county. By contrast, fewer than 1% of mail-in ballots -- or about 8,300 ballots statewide -- were rejected in the 2020 general election, according to the US Election Assistance Commission.

The decennial redistricting process has also added to primary night uncertainty -- and intrigue.

With a new congressional map designed to further reduce the number of contested seats on the map, most of both parties' nominees can expect that their primaries will be more fiercely fought than the contests that await in November. The diminishing number of swing districts means there has been an even greater focus on campaigns that cast opposing flanks of the parties against one another.

For Democrats, those contrasts have been on vivid display in the 28th Congressional District, where Rep. Henry Cuellar, one of the most conservative Democrats remaining in the House, is locked in a tight race with Jessica Cisneros, the 28-year-old immigration attorney backed by New York Rep. Alexandria Ocasio-Cortez and Vermont Sen. Bernie Sanders, who nearly ousted him from the South Texas seat in 2020.

Cuellar's district is modestly more Democratic this time around, but the primary appears to be even tighter -- and could be headed to a runoff with neither Cuellar nor Cisneros on track to clear 50%. In a cruel twist for the left, progressive candidate Tannya Benavides appears to have siphoned enough support from Cisneros to keep the contest with Cuellar close.

Cisneros had received a late boost in the race when it was revealed that Cuellar is under investigation by the FBI. Cuellar has denied any wrongdoing, and the specifics of the probe largely remain a mystery.

The signal to national Democrats from the South Texas showdown may be more clear, especially if Cuellar is able to overcome his legal concerns and defeat Cisneros again.

Republicans, including Trump, outperformed expectations with Latino voters in the 2020 elections and Cuellar has argued that his harder line on immigration issues, in a district that runs from the San Antonio suburbs down to the Rio Grande Valley and along the border to Laredo, is the only path for Democrats in the region. Victory for Cisneros -- and, should she win, the makeup of her coalition -- will provide new insight into what the shifting margins from two years ago portend for the fall elections. But no matter the outcome, the divisions in the party were clear from early in the night. Cisneros' backbone of support came from the San Antonio suburbs, while Cuellar dominated in the border counties -- a breakdown that will give both flanks of the party reason to celebrate and cause to fret.

The Republican primary for the 28th District was not decided Tuesday, with Cassy Garcia, a former staffer to Texas GOP Sen. Ted Cruz, advancing to the runoff, CNN projects. The second spot for that May contest had not yet been called as of midday Wednesday.

While Cuellar's bid for survival has captured the most attention, Republicans are also closely watching GOP turnout in other parts of South Texas after stepping up their recruitment of candidates to run in a region that has been dominated by Democrats for decades.

Monica De La Cruz, who pulled off a surprising finish when she came within 3 points of dispatching Democratic Rep. Vicente Gonzalez in 2020, will win the GOP nomination for the newly redrawn 15th District, CNN projects, bolstered by the endorsement of both Trump and House Minority Leader Kevin McCarthy.

The crowded Democratic race to face off with De La Cruz will be decided in a runoff. Afghanistan veteran Ruben Ramirez, a lawyer and former high school teacher backed by Gonzalez, has secured his spot, CNN projects, but it remains unclear whether John Villarreal Rigney, an attorney and owner of a South Texas construction firm, or Michelle Vallejo, a progressive small business owner endorsed by Massachusetts Sen. Elizabeth Warren, will be joining him.

Gonzalez is now running in the neighboring 34th District, which became more favorable for Democrats after redistricting. He will win his primary outright to move on the general election where he will face Mayra Flores, who will best three other candidates in the GOP primary, CNN projects.

Despite the uncertainty surrounding the Cuellar-Cisneros race, another progressive backed by Sanders and Ocasio-Cortez, former Austin City Council Member Greg Casar, will advance to November, CNN projects, after earning a comfortable majority in the Democratic primary for the 35th District, a safe blue seat.

On the Republican side, a perceived lack of fealty to Trump had endangered incumbent Reps. Van Taylor and Dan Crenshaw. Taylor's opponents in the 3rd District have attacked him over his vote to establish an independent commission to investigate the January 6 insurrection at the US Capitol. The panel was rejected by Senate Republicans and effectively replaced by a select committee created by House Speaker Nancy Pelosi. But Taylor's vote riled some Trump supporters, which fueled the opposition against him in his current race. Taylor will advance to a May runoff where he will face former Collin County Judge Keith Self, CNN projects.

Crenshaw, who ran unopposed in the 2020 GOP primary, triumphed over multiple challengers in the 2nd District attacking him from the right -- a consequence, in part, of Texas Republicans' gerrymandering of the district to make it a safe red seat. Crenshaw is one of the most conservative members in the GOP conference, and was a signatory to Paxton's 2020 election lawsuit, but he has occasionally sparred with the former President's closest allies, including Georgia Rep. Marjorie Taylor Greene, most recently criticizing her for speaking at a White nationalist conference over the weekend.

Greene and North Carolina Rep. Madison Cawthorn were also opposing GOP leadership in the race to replace retiring GOP Rep. Kevin Brady in Texas' 8th District. Former Navy SEAL Morgan Luttrell is the national party's choice, but far-right opponent Christian Collins had the backing of Greene, Cawthorn, Cruz, and Joe Arpaio, the former Maricopa County, Arizona, sheriff who was pardoned by Trump. The race was undecided as of Wednesday morning.

This story has been updated with additional developments.