Departments such as the Bureau of Engraving and Printing would have to furlough workers starting next week unless Congress approves a new spending bill this week. (Creative Commons)

A federal government shutdown appeared alarmingly close Tuesday morning as Republican leaders refused to accept a budget deal for the rest of this year "that fails to make real spending cuts."

Instead, House Speaker John Boehner (R-Ohio) proposed a continuing resolution funding the government from this Friday to next and cutting $12 billion. The previous stopgap measures that have kept the government running since the beginning of October have cut about $2 billion per week.

President Barack Obama said he would meet with Senate Majority Leader Harry Reid later Tuesday because "there's no reason" an agreement for the rest of the year "shouldn't get done." He said two-week budgets and other stopgaps are no way to run government.

"We don't have time for games or to score political points, at least on this," Obama said. "We can't have a my way or the highway approach to this problem."

The only circumstance in which he would accept a temporary measure is if it was for one or two days to leave enough time to vote on a wider measure.

Because bills must be posted online 72 hours before they are considered, Congress faces a midnight deadline to reach some sort of agreement. Without one, there appear few ways for government agencies to operate normally after Friday.

One of the Tea Party's leaders criticized Congressional leaders who met Tuesday morning with Obama, saying a government shutdown isn't the right thing to do. One of the effects she said would be interest rates on government debt going up because of missed payments.

Keeping that debt from going out of control is one of the the central themes in Rep. Paul Ryan's budget proposal for next year, which he unveiled Tuesday as his colleagues met with Obama.

To reach reporter Paresh Dave, click here.

Find him on Twitter: @peard33.