TOPEKA — Gov. Sam Brownback’s departure would shake up the Statehouse, offering a chance for the Legislature to forge a better relationship with the executive branch, but might not significantly alter the dynamics of ongoing policy fights.

Brownback declined to comment Thursday after sources told various news outlets he is in talks to take a United States posting in Rome coordinating food and agricultural work with the United Nations.

But chatter swept through the Statehouse over potential fallout from a gubernatorial resignation, which would elevate Lt. Gov. Jeff Colyer, a Johnson County plastic surgeon at Hays native, into the administration’s top job.

For their part, Brownback and Colyer did little to tamp down speculation. They declined to either confirm or deny Brownback has had discussions about the post. Brownback also declined to comment when asked if he would commit to staying through the end of the legislative session.

“I’m just not going to make comments on any of that,” Brownback said, before adding President Donald Trump’s administration is “off to a strong start on job creation and security issues.”

Brownback took questions after presenting a Kansas Humanitarian of the Year award to Luther Fry, a Garden City ophthalmologist who has provided extensive charity care. Asked if the position, which would involve leading the U.S. Mission in Rome, would be a good fit, Brownback said he believes in humanitarian work.

If Brownback departs, it would come at a momentous time in Topeka. Lawmakers are seeking to close a budget shortfall next year of hundreds of millions of dollars, likely through tax increases. Brownback vetoed one plan last month, and his veto was only barely sustained in the Senate.

At the same time, lawmakers have until June 30 to enact a new school funding formula. The Kansas Supreme Court set the deadline last week in a ruling that found funding levels inadequate.

Colyer didn’t offer a direct answer when asked if he would be committed to Brownback’s policy agenda.

“I’m sitting here doing my job here. I’m working with the governor every day on things. We’re working on solutions, and that’s what I’m after, and that’s what the governor’s after,” Colyer said. “We’re going to keep doing that.”

Some moderate Republicans and Democrats believe a change in executive leadership could alter the atmosphere in the Statehouse.

Rep. Stephanie Clayton, R-Overland Park, has been critical of Brownback. She described herself as “cautiously optimistic” about a potential change.

“With the lieutenant governor, it’s an unknown, and with the current governor it’s a known,” Clayton said. “I know he’s going to veto things. I don’t know if the lieutenant governor will veto things.”

The state’s financial crisis will be Brownback’s legacy, whether he leaves tomorrow or in 18 months, said House Minority Leader Jim Ward, D-Wichita. Whether Colyer would spend his political capital on preserving the 2012 tax policy — which lawmakers have voted to largely repeal — or works with lawmakers is the question, Ward said.

Brownback has been involved in Kansas politics for decades and has built a network of supporters, Ward said. A number of people who work in Republican politics got their start on Brownback campaigns, he added.

Colyer, on the other hand, lacks that “footprint,” Ward said.

“It changes the dynamic in the building,” he said.

Senate Vice President Jeff Longbine, R-Emporia, said he didn’t know how Colyer might alter policy.

“I think it’s yet to be seen, yet to be determined,” Longbine said. “If there is a change, does Lt. Gov. Colyer come in, further the goals and policies and thought processes of the Brownback administration, or does he try to put his own signature on it? I don’t know.”