Even though congressional support for elevating the Veterans Administration to the Cabinet is unwavering, senators yesterday questioned whether the plan would unduly politicize the agency by creating a new, unnecessary layer of political appointees.

VA Administrator Thomas K. Turnage told the Senate Governmental Affairs Committee that the new department should be headed by up to 12 presidential appointees. There are only three at the agency now.

When committee Chairman John Glenn (D-Ohio) asked whether that wouldn't lead to a politicization of the agency, Turnage responded that the change would be necessary to give the VA "greater flexibility."

Harry Walters, who preceded Turnage as Reagan's VA administrator, told the panel that presidential nominees would be good for the VA since "the confirmation process would give the Senate a chance to look at the credentials of the appointees."

Sen. John Heinz (R-Pa.) suggested that the move to increase the number of political appointees is just "one more instance of the VA wanting a free hand to do anything it wants."

Max Cleland, who headed the VA in the Carter administration, testified that he believes it is "quite adequate" to restrict the number of presidential appointees in the proposed new department to three: the administrator, deputy administrator and inspector general.

Last month, the House voted 399 to 17 to approve legislation making the VA a department with Cabinet-level status after President Reagan endorsed the move, a change that veterans' groups have promoted for many years.

The groups and their supporters have said that in addition to showing increased visibility and respect for veterans, a new Cabinet-level department is needed for an agency as large as the VA. They noted yesterday that 78 million Americans -- 27 million veterans and 51 million dependents and survivors, making up more than one-third of the population -- are eligible for VA benefits.

With more than 220,000 employes, the VA is second in size only to the Defense Department, said Sen. George J. Mitchell (D-Maine). It has more facilities nationwide than any other federal agency except the Postal Service.

Cleland, who testified in favor of making the VA a Cabinet-level department, said that Carter recognized the VA needed more access to high-level policymaking and signed an executive order to allow Cleland to attend Cabinet meetings, a practice that was ended by the Reagan administration.

"I sat in the cheap seats around the wall. I didn't sit at the table with the president," Cleland said, adding that he was not a full member of the Cabinet. But he said Carter's decision opened "my window to the world, not only providing insight into what the president was thinking and what was happening in the federal government but, more importantly, insight into what I and my agency could do to serve America's defenders and their families.

"In contrast, when a VA administrator does not have access to the president and to the functions of the government, he can find himself -- and the agency -- isolated in the bureaucracy and getting 'lost in the shuffle,' ultimately causing the agency and its mission to suffer," Cleland said.

Turnage said that although he supports the change, he had never directly asked Reagan to be added to the Cabinet or even to be allowed to sit in on Cabinet meetings.

Because of the power of the veterans' lobby, the Senate is virtually sure to approve a Cabinet-level VA, but several members of Congress have made it clear that they expect the agency to be accountable.

Glenn warned that although the agency enjoys bipartisan support, any attempt to politicize it or drive up its budget is taking a chance on "lousing up a good situation."

Rep. Jack Brooks (D-Tex.), who managed the House bill, told the committee, "This is a great deal, and it's not going to do any harm to anybody." But he said he expects to see some VA budget tightening: "I expect them to shape up if they're going to be wearing those fancy suits."

A number of veterans' groups testified or submitted statements in favor of the change, including the Vietnam Veterans of America, whose spokesmen said the change is needed so the VA will have the clout to resist cost-cutting plans virtually imposed on the agency by the Office of Management and Budget.