Republican voters in Kansas rebelled against the policies of Gov. Sam Brownback on Tuesday, ousting his fellow conservatives in at least 11 state legislative primary races amid widespread angst about Kansas’s financial situation.

With some races still undetermined on Wednesday, but also leaning toward moderates, the primary was a tangible sign of the grumblings that have been going on under the surface in heavily Republican Kansas, as deep cuts to taxes, a centerpiece of the Brownback agenda, have left the state short on revenue and led to cuts to government services.

“People, they were frustrated,” said Dinah Sykes, a moderate Republican from the Kansas City suburbs who defeated the conservative incumbent in her State Senate district. “They were ready for people to listen to them and be accountable to them.”

The results promised to reshape the dynamics in the Legislature, which has been dominated in recent years by conservatives friendly to Mr. Brownback, and perhaps add pressure for the governor to reconsider some of his tax policies, which were predicated on a supply-side theory of economics and championed by conservatives nationally. Kansas has repeatedly missed revenue collection targets, has seen its credit rating slashed and has cut funding for some government services during Mr. Brownback’s tenure.