The Associated Press
The secretary also blamed delays in passing the measure on President Barack Obama having to spend "far too much time talking about what's not in the bill" and trying to counter "wild accusations" by Republicans.
Sebelius said she believed the deadline would hold but indicated the president would not walk away from the key agenda item of his presidency should the House not act by then.
She said Obama still hoped for some Republican votes on the health care bill, "but I'm not sure there will be."
The fundamental conflict, she said, centers on Republican beliefs that "insurance companies should have less regulation than they do now, less consumer protection, less oversight."
Republicans argue that the Obama plan amounts to a government takeover of the U.S. health care industry and would increase an already burgeoning budget deficit.
Another stumbling block arose with renewed objections by Rep. Bart Stupak (D-Mich.) over what he sees as federal funding for abortion in the Senate bill. The White House and most of those who support the measure insist that is not true.
Sebelius said "conversations will continue" if necessary to overcome Stupak objections. He has insisted on a House-passed plan that says no health insurance plan receiving federal subsidies can pay for abortion, except under exceptions already allowed by federal law.
Sebelius appeared on ABC's "This Week" and NBC's "Meet the Press."
Meanwhile, Rep. Chris Van Hollen (D-Md.), who heads the House Democrats' campaign team, said House members are waiting for the final plan and its analysis by the Congressional Budget Office before deciding to support it.
"I believe it will pass. Do we have a mortal lock? No," Van Hollen said. "But I think the trend is in the right direction because people see that the status quo is absolutely broken."
Three House Democrats who voted against the bill appeared open to considering changing their votes, but none committed to supporting the Senate legislation.