(CNN) -- It's "just the tip of the iceberg." That's what a congressional committee chairman investigating allegations of delayed care and cooked books at Veterans Affairs health care facilities told CNN.
Rep. Jeff Miller, a Florida Republican who heads the House Veterans Affairs panel, on Thursday forecast more serious developments in the national program serving nearly 9 million veterans.
"We've received some information and some tips that will make what has already come look like kindergarten stuff," he told CNN's New Day.
The controversy has broadened since CNN first reported six months ago on allegations of alarming shortcomings within the VA medical care system that potentially have had deadly consequences in dozens of cases.
Developments taking shape on Thursday included a meeting later in the day between embattled Veterans Affairs Secretary Eric Shinseki and the No. 2 Democrat in the Senate, Richard Durbin of Illinois.
Shinseki, who has come under pressure from some quarters to step down, told reporters after the meeting that he has not offered his resignation to President Barack Obama, who is standing by him.
He later issued a statement to the nation's veterans stressing that the entire matter is the subject of an internal review and an independent investigation.
"The reports of veterans' negative experiences while seeking VA care are of great personal concern to me" and promised action if "any allegations under review are substantiated," he said.
"As we approach our observance of Memorial Day and its special significance to our nation, VA is re-doubling its efforts, with integrity and compassion, to earn your trust," he added.
No shows at meeting
The top Republican in Congress weighed in on Thursday with his concerns about allegations of systemic problems at the VA.
"I have not called for General Shinseki to resign although I have to admit I am getting a little closer," said House Speaker John Bohener. "But here is the point: This isn't about one person. This isn't about the secretary. It is about the entire system underneath him."
Also on Thursday, Robert Jesse, the VA deputy undersecretary, met with members of the House Health Care and Wellness Committee, but three senior VA officials asked to meet with Miller's committee didn't show up.
The VA said the committee didn't give it enough notice, an explanation Miller called disingenuous.
"My intent is to go ahead and subpoena them" for a hearing before his committee on May 30, Miller said.
The officials were identified as Dr. Thomas Lynch, an assistant undersecretary for health and clinical operations; Joan Mooney, an assistant secretary for congressional and legislative affairs, and Michael Huff, a congressional relations officer.
Miller has accused the VA of failing to adequately respond to his panel's May 8 subpoena, which included a request for information about the alleged destruction of a secret waiting list for care at the Phoenix Veterans Affairs Health Care System.
In a statement to CNN, the VA said it "is committed to working with the committee to provide relevant information expeditiously" and that it has "produced over 3,000 pages of documents to the committee" so far.
Separately, Sen. Marco Rubio sought to advance a proposal that would change federal rules to make it easier to fire VA executives. Similar legislation was approved by the House on Wednesday.
Rubio said that Shinseki should have the power to hold people accountable. "Give the secretary the power to fire employees underneath him who are not doing their jobs," he said. "This is a matter of urgency."
Obama speaks out
The overall scandal prompted a response on Wednesday from Obama, who expressed dismay and demanded accountability, but also said he needed more time to find out what was going on.
"If these allegations prove to be true, it is dishonorable, it is disgraceful, and I will not tolerate it, period," Obama said.
Obama noted that the public wants a "swift reckoning" on the VA issue, but he defended the record of his administration and Shinseki.
On Wednesday, it was disclosed that some veterans hurt in combat in Iraq and Afghanistan are being made to wait for months to be seen in Phoenix, despite a mandate that they be give priority, according to a VA doctor.
Dr. Katherine Mitchell, the medical director of the Phoenix VA's post-deployment clinic, outlined the allegations on CNN's "AC 360."
Probing record keeping, lists
CNN reported last month that in Phoenix, the department used fraudulent record-keeping -- including the alleged secret list -- that covered up excessive waiting periods for veterans, some of whom died in the process.
The list in Phoenix was part of an alleged scheme designed by VA managers there who were trying to hide that 1,400 to 1,600 sick veterans were forced to wait months to see a doctor, according to a recently retired top VA doctor and several high-level sources.
Overall, the number of VA facilities under investigation has expanded to 26, the agency's Office of Inspector General said Tuesday.
An internal VA memo from 2010 showed officials warned of "inappropriate scheduling practices" to cover up excessive waits for veterans four years ago. But the CNN investigation shows such practices have continued.
The VA has acknowledged 23 deaths nationwide due to delayed care, and the agency's inspector general has launched an investigation of the Phoenix allegations that involve up to 40 other deaths.
At a Senate hearing last week, the inspector general said his investigation so far found a possible 17 deaths of veterans waiting for care in Phoenix but added there was no evidence that excessive waiting was the reason.
Obama said Wednesday that the cooked books and excessive waits applied more to veterans with chronic conditions who are among the 85 million VA appointments each year instead of those needing emergency attention.
CNN's Nelli Black, Paul Courson, Deirdre Walsh, Ted Barrett, Jim Acosta, Virginia Nicolaidis and Becky Brittain contributed to this report.