His voice cracking, Boehner said veterans "are men and women who served our country, and we've not just let them down, we've let them die. This is awful stuff, and someone ought to be held accountable for it."
Boehner has not called for Shinseki to resign, but he said, "I have to admit that I am getting a little closer" to doing so.
House Minority Leader Nancy Pelosi, meanwhile, called allegations of misconduct at the VA "completely and utterly unacceptable" and urged a broad review of services for veterans.
Pelosi, D-Calif., said she was open to an idea advanced by Sen. John McCain, R-Ariz., to allow veterans to receive medical care at private hospitals.
"We can't have another backlog of people waiting for permission to go to a federally qualified clinic in a region," she said. "We have to think in a big way because this is a very big challenge."
Obama's deputy chief of staff, Rob Nabors, was in Phoenix Thursday to meet with hospital staff. The director of the Phoenix VA Health Care System has been placed on leave while the inspector general investigates claims that up to 40 people died while awaiting treatment in Phoenix.
In the South Dakota Senate campaign, Weiland forcefully called for Shinseki to step down. But he also criticized House Republicans for temporarily shutting down much of the government last year.
"Anyone who does not understand that it is the penny-pinching stupidity and arrogance of the 'shut it down' politicians in Congress that is the real problem is either blind or willfully ignorant," Weiland said in a statement Thursday.
Among the Republicans calling for Shinseki's resignation is Mike McFadden, who hopes to take on Sen. Al Franken, D-Minn.
Associated Press writers Brian Bakst in Minneapolis and Jim Kuhnhenn and Erica Werner in Washington contributed to this report.
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