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It has been two days since Senator Ted Cruz of Texas swept Colorado’s delegates, and Steve House, the chairman of the state’s Republican Party, is feeling the wrath of Donald J. Trump’s supporters.

In fact, his cellphone will not stop ringing.

Mr. House has been hearing from angry voters from across the state and country who say they think the will of the people was ignored because Colorado’s system of caucuses, a multistep process that ended on Saturday, left the selection of the state’s presidential nominating delegates to party activists.

Mr. Trump, who was shut out in Colorado, has complained that the system was rigged, and since Sunday night Mr. House has received more than 2,000 calls from people complaining that the process was a sham. His telephone number was mysteriously disseminated across the Internet.

“It was done exactly according to the rules,” Mr. House said, denying claims of underhanded or manipulative tactics.

For Colorado Republicans the backlash came as something of a surprise because the party decided last August to do away with its presidential straw poll. After the Republican National Committee decided that the outcome of state straw polls would have to result in bound delegates, the state party decided that it would be too risky to use that kind of system because of potential problems counting that many ballots without state resources.

Colorado had a presidential primary election as recently as 2000 but abandoned it because of the costs. The state Republicans held straw polls in 2008 and 2012, but the results were not binding. State Democrats have kept their straw poll.

Mr. House acknowledged that there are a lot of deeply entrenched players within the party who think the system works well and believe that those who are the most politically engaged should determine who becomes the party’s presidential nominee.

“If I tried to get rid of the caucus, they’d string me up,” Mr. House said.

Until now voters have not made a huge deal about the current system. However, Mr. House expects that the ferocity of the criticism that Colorado is facing will push state legislators to make changes before 2020.

“They have not asked for a presidential primary to be put back in play in a way that got their elected officials to do something about it,” Mr. House said, explaining that Colorado voters have the ultimate say in determining the system.

In the meantime, the Colorado Republican Party is weathering the blowback. Mr. House said that he was investigating how an official Twitter account was hacked by someone who tweeted #NeverTrump. And, for now, he has no plans to change his cellphone number.

“You shut the phone off at some point,” he said.

