(Jim Lo Scalzo/EPA)

Veterans Affairs Secretary Eric K. Shinseki apologized Friday morning for the “indefensible” troubles plaguing the agency’s health-care system, but he also put Congress on the spot, asking lawmakers to fill top vacancies at the department.

“And I ask the support of Congress to fill existing VA leadership positions that are still vacant,” he said near the end of his remarks at the 2014 National Coalition for Homeless Veterans annual meeting.

Confirming White House executive branch nominations isn’t exactly the Senate’s strong suit these days. The Shinseki plug could be interpreted as a little dig at the sluggish process as more and more members of Congress say he should resign.

There are only two VA nominations pending in committee and one awaiting floor action, according to the Senate Web site.

1. Under secretary for health

In the wake of the Phoenix hospital scandal, the agency’s top health official, Robert Petzel, was asked to resign. At the beginning of the month, the White House nominated Dr. Jeffrey Murawsky as his replacement. Murawsky  heads a VA hospital network in the Midwest. The White House says he was selected by a formal commission that includes outside experts, but his nomination is not without controversy. One of the hospitals under his jurisdiction allegedly also falsified its waiting lists. The Veterans Affairs Committee has not scheduled a vote on him.

2. Chairman of the board of veterans’ appeals

The White House nominee to head the board that hears benefit appeals from veterans has been awaiting committee confirmation since January 2012. Constance Tobias  serves as chairwoman of the appeals board at the Health and Human Services Department.

3. Assistant secretary of Veterans Affairs (policy and planning)

The office, which lists among its responsibilities  advancing “veteran health care by providing high quality data and analyses to facilitate strategic planning and decision making across VA,” has been without a formal leader since January 2013. The president’s nominee, Linda Schwartz, passed through committee unanimously in November 2013, but is stuck in Senate floor purgatory.

4. Secretary of Veterans Affairs (UPDATED)

This position has now been open for about two hours at the time of this update.