"While no one can predict with certainty how the current shutdown will be resolved, I am confident that if we keep advancing common-sense solutions to the problems created by the shutdown that Senate Democrats and President Obama will eventually agree to meaningful discussions that would allow us to ultimately resolve this impasse," Cantor said in the memo that a GOP source made available to CNN.
A conversation between two conservative GOP senators showed Republicans think they can win the debate. In the comments caught by live microphone, tea party-backed Sen. Rand Paul told his Kentucky Republican colleague, Minority Leader Mitch McConnell, that continuing to hammer Democrats for refusing to consider GOP proposals would eventually succeed.
Proposal from moderates
Meanwhile, two moderate House members -- one Republican and one Democrat -- proposed a compromise Thursday that would fund the government for six months while eliminating a tax on medical devices in the health care reforms.
Senate Democrats quickly rejected the idea because it would link the health care reform provision to the need to fund the government now while extending deep mandatory budget cuts they oppose for half of the new fiscal year.
Instead, Obama -- who canceled a trip to Brunei and Indonesia for this weekend's Asia-Pacific Economic Cooperation summit because of the ongoing shutdown -- and other Democrats have said they want to negotiate a broad budget deal that could include tax reforms and other matters. But they're only willing to engage in such talks after the government reopens.
This already slogging debate over what to do about the crisis ground to a halt Thursday because of something that, at first glance, did not directly involve any of the legislators on Capitol Hill, even if it did hit very close to home.
A chase that began at a White House security checkpoint ended near the U.S. Capitol Hill when authorities opened fire on a car containing a woman and a child, an intelligence source told CNN.
Two police officers suffered injuries in the ordeal, according to D.C. Police Chief Cathy Lanier. The female driver -- who didn't fire any shots herself, according to multiple sources -- died of gunshot wounds.
The House and Senate were both put on lockdown, with no one allowed to leave or enter Capitol Hill buildings and everyone urged to steer clear of windows and doorways, for about an hour.
Not long after, Democrats and Republicans reconvened on the House floor and, in a rare show of unanimity, thanked the responding officers.
Then they resumed their normal business -- which, if the past few weeks is any indication, meant more blame and little agreement on how to bring the government back on line.