AUSTIN (Nexstar) -- Among the Texans positioned to take on powerful posts in the new Trump era of Washington politics, few were seen as more likely ascendants than U.S. Sen. John Cornyn and Texas Attorney General Ken Paxton. Neither are set to get there after Wednesday. Cornyn, for his part, hoped to succeed Mitch McConnell as Senate Majority Leader. He fell to South Dakota's John Thune by just three votes in the Senate GOP's secret ballot Wednesday morning. "Congratulations to my colleagues who will be leading the Senate Republican Conference next Congress, and thank you to those who supported me," Cornyn wrote on X.   We are united and prepared to enact President Trump’s agenda on day one, and I look forward to working alongside my colleagues to take advantage of the opportunities we will have next year to confirm nominees, address our national debt, extend the Trump tax cuts, and reverse the Biden-Harris administration’s disastrous border policies." Sen. Cornyn looks ahead to race for GOP leader  On Wednesday afternoon, President-elect Trump tapped U.S. Rep. Matt Gaetz, a firebrand Florida Republican, to lead the Department of Justice as Attorney General. Paxton's close relationship with Trump and his record of lawsuits on behalf of the former president suggested to many that he would be on the shortlist for AG. "I am excited to work with my friend Matt Gaetz," Paxton wrote on X after the announcement. "There are few people I trust more to take on the deep state and end the weaponization of the justice department. Matt Gaetz has been a stalwart defender of liberty, and Texas has his back. Congratulations, Matt." Agriculture Commissioner Sid Miller is also considered a top pick to run the U.S. Department of Agriculture. He was closely considered for the job ahead of Trump's first term. "I think both Miller and Paxton have been waiting for this moment," Professor of Political Science at the University of Houston Brandon Rottinghaus said. "They know that they're in Trump's orbit, and they may not get the nod because there are a lot of people who may want that, but it's certainly the case that they've set themselves up perfectly for a spot in Trump's administration." As for Cornyn, political observers are now speculating whether the 74-year-old will run for a fifth term in 2026. He's expected to face a trying primary challenge from Texas' most conservative flank and may not see another chance to ascend to leadership. "He said he'll run again, and I take him at his word, but it's definitely going to be something he's going to have to come into with eyes open," Rottinghaus said. Texas is changing politically. Donald Trump definitely has a greater sway than he's ever had... They want to see a Ted Cruz and not a John Cornyn. That's where Republican primary voters are. So we're definitely going to see a competitive race in the primary."