Former House Speaker Newt Gingrich, whose faceoff with Clinton led to government shutdowns that inflicted significant damage on the GOP and helped resurrect the then-president's political fortunes in time for his 1996 re-election bid, said his GOP colleagues should not yield.
"This is not a dictatorship. Under our constitution, there should be a period of tension and there should be a compromise on both sides," Gingrich said.
Robert Reich, who was Clinton's labor secretary, said that works only if both parties are willing to negotiate.
"Sorry, under our constitutional system you're not allowed to risk the entire system of government to get your way," Reich said.
It is likely that when the House legislation arrives in the Senate, Democrats there will strip off the health care defunding mechanism. Democrats plan to send back to the House a bill that prevents disruptions in government services but not the health provision they championed.
Cruz, however, said Senate Republicans cannot allow that to happen and should mount every procedural hurdle available. Cruz, who pushed lawmakers to tie a budget bill with health care hurdles, said Republicans should mount a procedural roadblock that would require 60 votes for any changes to the House bill.
"You know what? If Senate Republicans stand together, we can stop Harry Reid from doing it," Cruz said.
But within his own party, Cruz faced skepticism.
"It's not a tactic that we can actually carry out and be successful," said Sen. Tom Coburn, R-Okla. "The answer now in the Senate, by those who propose this strategy, is to filibuster the very bill they said they wanted."
Pelosi spoke to CNN's "State of the Union." Cruz and McCaskill were interviewed on "Fox News Sunday." Reich, Gingrich and Graves appeared on ABC's "This Week." Coburn was on CBS' "Face the Nation."