Justices take their seats to hear oral arguments in a judicial funding case before the Kansas Supreme Court in Topeka, Kan., Thursday, Dec. 10, 2015.

Topeka ? Top Republicans in the Kansas House plan this week to test the support for changing how state Supreme Court justices are selected to potentially give the governor and legislators more influence.

“We’ll see where people are,” House Speaker Ray Merrick, a Stilwell Republican, told The Associated Press on Monday. “We’ll see what their ideas are.”

House Republicans have scheduled a caucus meeting for Tuesday for a briefing on state Supreme Court decisions in individual capital cases in 2014 that overturned death sentences — rulings that spurred calls for a change. They also have a caucus meeting planned Wednesday on judicial selection issues, and the House Judiciary Committee has a briefing on the capital cases Wednesday afternoon.

Gov. Sam Brownback has described the current selection system as undemocratic and has called publicly for overhauling it, a sentiment shared by the anti-abortion group Kansans for Life, which is influential with GOP lawmakers.

Supporters of the judicial selection current process believe the conservative Republican governor and his allies are trying to push the Supreme Court to the right — or, as Rep. John Carmichael, a Wichita Democrat and attorney, said, seeking change so Brownback “can put his thumb on the judiciary.”

A nominating commission screens applicants for Supreme Court vacancies and names three finalists. The governor must pick one; there is no state Senate confirmation or other role for lawmakers. Five of the nominating commission’s members, including its chairman, are attorneys elected by other attorneys.

The House Judiciary Committee last year approved rival proposals, meaning the full chamber can debate them. One calls for the partisan election of Supreme Court justices, and the other would abolish the nominating commission and have the governor make the appointments, subject to Senate confirmation.

Changing the selection process requires amending the Kansas Constitution, and a proposal must be adopted by two-thirds majorities in both chambers and approved by a simple majority of voters in a statewide election. The GOP has supermajorities in both chambers, but Democrats and enough moderate Republicans have opposed changes to keep a measure from passing the House.

“I’m hoping to increase the temperature to where we find out that people are ready to do the right thing,” said House Majority Leader Jene Vickrey, a Louisburg Republican.

The state’s voters approved the current selection system as a constitutional amendment in 1958, replacing the election of justices. Supporters argue that the system has minimized partisan politics in the selection process and accuse GOP conservatives of seeking to limit judicial independence.

But Brownback spokeswoman Eileen Hawley said the governor is calling for “a more democratic process.”

The first House GOP caucus and the Judiciary Committee briefing will focus on the cases of Jonathan and Reginald Carr, two brothers who were sentenced to die for four murders in Wichita in December 2000 following a night of mayhem in which they sexually abused and robbed their victims.

The Kansas Supreme Court overturned their death sentences in July 2014, partly because the brothers didn’t have separate sentencing hearings. The decisions generated widespread criticism, including from Brownback and Republican legislators, and last week the U.S. Supreme Court overturned the Kansas court’s decisions.