In paragraph 3, corrects name of Manhattan judge hearing case to Jeannette Vargas, not Paul Engelmayer

By Luc Cohen and Tom Hals

NEW YORK, Feb 14 (Reuters) - Two federal judges will consider on Friday whether Elon Musk's government cost-cutting team known as DOGE will have access to Treasury Department payment systems and potentially sensitive data at U.S. health, consumer protection and labor agencies.

The Musk-led Department of Government Efficiency has swept through federal agencies since Republican Donald Trump became president last month and put the chief executive of carmaker Tesla TSLA.O in charge of rooting out wasteful spending as part of Trump's dramatic overhaul of government.

In Manhattan, U.S. District Judge Jeannette Vargas will consider a request by Democratic state attorneys general to extend a temporary block on DOGE that he put in place on Saturday, which prevented Musk's team from accessing Treasury systems responsible for trillions of dollars of payments.

The states allege that Musk's team has no legal power to access the payment systems that contain sensitive personal information on millions of Americans.

The lawsuit also argued that Musk and his team could disrupt federal funding for health clinics, preschools, climate initiatives and other programs, and that Trump could use the information to further his political agenda.

In Washington, U.S. District Judge John Bates will consider a request by unions to prevent the DOGE team from accessing sensitive records at the Department of Health and Human Services, the Labor Department and the Consumer Financial Protection Bureau.

Bates denied a similar request last week, delivering a ruling in the Trump administration's favor. The unions have renewed that request after they amended their lawsuit.

A similar group of Democratic attorneys general sued Musk, Trump and DOGE on Thursday, alleging that Musk's appointment was unconstitutional. The attorneys general asked a federal judge in Washington to bar him from accessing and using government data, cancelling contracts or making personnel decisions, among other things.

Most of Trump's initiatives that have been legally challenged have been blocked by the courts, which has prompted Musk and other Trump allies to call for judges to be impeached, although the president said he would obey court orders.

Despite some initiatives being blocked in court, Trump's administration has pushed ahead with mass firings of government workers and has sharply curtailed the United States' foreign aid program, although the cost-cutting appears to be focused on programs opposed by political conservatives.

(Reporting by Tom Hals in Wilmington, Delaware, and Luc Cohen in New YorkEditing by Matthew Lewis)

((thomas.hals@thomsonreuters.com; 610-544-2712))