UPDATE: The Senate voted 53-45 Saturday to block a Democratic bill that would have raised the debt ceiling until after the 2014 elections.

House Republicans reacted bitterly Saturday after it became apparent that President Obama had rejected their offer to raise the debt ceiling and address the government shutdown in favor of negotiating with a bipartisan group of senators.

A small group of Senate Democrats and Republicans, led by Sens. Susan Collins, R-Maine, and Joe Manchin, D-W.Va., began developing their own plan after growing impatient with a budget impasse that led to a government shutdown now in its 12th day and Thursday's looming deadline to raise the debt ceiling to avoid defaulting on the nation's $16.7 trillion debt. Talks with the White House were ongoing Saturday.

House Republicans are angry with Senate Republicans, believing their willingness to negotiate a funding and debt deal with Senate Democrats undermined the House's position in talks with Obama. The House majority decided in a closed-door meeting Saturday morning to standing firm on their existing offer to raise the debt ceiling and to encourage Senate Republicans to negotiate a deal acceptable to the House.

“I’m disappointed that the president has rejected the offer that we put on the table. I know he is trying to see which Republican senator he can pick off in the Senate. I hope that the Senate Republicans stand strong so we can speak with one voice,” House Majority Leader Eric Cantor, R-Va., said.

“I’m hoping that the Senate is standing strong and that we Republicans can speak with one voice,” Cantor added.

House Republicans are privately concerned about being jammed by the Senate at the 11th hour. The federal borrowing limit must be raised by Thursday to avoid default, and House Republicans would be in a difficult political position if the Senate sends them a bipartisan bill close to that deadline.

The one effective message the GOP has had through the government shutdown and the debt ceiling debate was that Obama was refusing to even negotiate with the congressional Republicans. A bipartisan Senate agreement negotiated with the White House eliminates that talking point. That could put Republicans in the unsustainable position of explaining why they blocked a deal that would have reopened the government and averted another economic crisis.

But House Republicans insist they would not support a Senate bill they determine does not go far enough in addressing the nation's rising debt and deficit. House Republicans are also holding out for some proposal related to Obamacare, such as the repeal of the medical device tax.

House Republicans also did not rule out supporting a bipartisan Senate deal.

“We'll have to make that decision based on what they send us," Rep. Trent Franks, R-Ariz., said.

Senate Republicans were meeting Saturday to plot their next steps. Around noon, the Senate was scheduled to hold a key procedural vote on a one-year, $1 trillion debt ceiling increase with no strings attached. That vote was expected to fail.