WASHINGTON — It is the hate that dare not speak its name.

Since his arrival in 2013, Senator Ted Cruz, Republican of Texas, has managed to alienate, exasperate and generally agitate the plurality of his 99 colleagues in the Senate. In a highly partisan, hypercompetitive legislative body where solipsism is nearly a creed, Mr. Cruz stands out for his widely held reputation for putting Ted first.

“I don’t think he’s been effective,” said Senator John McCain, Republican of Arizona, chairman of the Senate Armed Services Committee, and the party’s nominee for president in 2008. “I think that’s pretty obvious. Shutting down the government? How did that work out?”

Mr. Cruz is so unpopular that at one point not a single Republican senator would support his demand for a roll-call vote, known as a sufficient second, leaving Mr. Cruz standing on the Senate floor like a man with bird flu, everyone scattering to avoid him.

In his presidential campaign, Mr. Cruz uses his role as an outsider as a source of strength. “It shouldn’t surprise anyone that the Washington establishment is against the candidacy of Ted Cruz,” said Rick Tyler, a spokesman for Mr. Cruz’s presidential campaign. “We are not looking for the approval of the Washington cartel.”