Updated: 3:36 p.m.

A Justice Department lawsuit challenging Arizona’s new immigration law has prompted jeers from many Republicans on Capitol Hill and a mixed bag of responses from Arizona Democrats.

Arizona’s two Republican Senators are questioning the Obama administration’s commitment to border security in light of the lawsuit, filed Tuesday afternoon in U.S. District Court in Phoenix. Sens. Jon Kyl and John McCain issued a statement saying it was “far too premature” for the administration to challenge the new law in court, since it does not take effect until later this month.

“The American people must wonder whether the Obama Administration is really committed to securing the border when it sues a state that is simply trying to protect its people by enforcing immigration law,” the Senators wrote. Kyl and McCain have defended the state law as necessary by arguing that federal efforts to secure the border with Mexico have been inadequate.

The Justice Department sued Arizona and asked a federal judge to prevent the law from taking effect until the lawsuit has been decided. The department argues that the new immigration law runs afoul of the pre-emption doctrine entailed in the Constitution’s Supremacy Clause, which dictates that federal law supersedes state statutes. “The Constitution and federal law do not permit the development of a patchwork of state and local immigration policies throughout the country,” Justice Department officials wrote in a 54-page brief.

Justice Department officials argued that permitting a hodgepodge of state and local policies would make it difficult for the federal government to enforce federal immigration laws.

Kyl and McCain said the lawsuit’s basis is faulty. “The Obama administration has not done everything it can do to protect the people of Arizona from the violence and crime illegal immigration brings to our state,” they wrote. “Until it does, the federal government should not be suing Arizona on the grounds that immigration enforcement is solely a federal responsibility.”

The lawsuit also quickly drew fire from House Minority Leader John Boehner (R-Ohio), House Republican Study Committee Chairman Tom Price (Ga.) and House Judiciary ranking member Lamar Smith (R-Texas).

“The people of Arizona have a right to enforce their own laws, especially if the federal government is failing to live up to its responsibilities,” Boehner said in a statement Tuesday.

Criticism also came from two Arizona Democrats in competitive races. Rep. Ann Kirkpatrick called the lawsuit “a sideshow” that would distract “from the real task at hand,” while Rep. Harry Mitchell said that he was “disappointed” and that the administration had chosen the “wrong direction.”

Members of the Congressional Hispanic Caucus, meanwhile, have been urging the administration to mount a legal challenge to the law, which they say underscores the need for Congress to act on a comprehensive immigration overhaul. Caucus Chairwoman Nydia Velázquez (D-N.Y.) said the Justice Department rightly had “made it clear that state laws which violate the Constitution will not go uncontested.”

One of the most vocal opponents of the law, Rep. Raúl Grijalva (D-Ariz.), applauded the lawsuit, as did organizations including the American Civil Liberties Union and the American Immigration Council.

“This is exactly the right time for our federal government to send a message about the importance of fairness and equality under the law,” Grijalva said. “I join many others in thanking the president for his outreach and his leadership, and I look forward to working with him to ensure that justice is done for the people of Arizona and the country.”