But Sessions said those numbers together exceed the 2012 CBO baseline by $14 billion, and said Conrad's total spending proposal for 2013 lines up with proposed spending increases made by President Obama.

Senate committees could use those numbers to write appropriations bills that spend more money. If that happens, Sessions said he would try to raise points of order against those bills.

"I plan to pursue a vote on the inflated spending levels," Sessions said on the Senate floor. "In this first year since the passage of the debt deal, will we adhere to its modest restrictions, or will we blink?"

It remains to be seen whether the Senate will put forward any 2013 spending bills under the levels filed by Conrad. If they are considered, Senate Democrats might easily override his point of order, but Sessions said he would nonetheless work to find ways to ensure the Senate does not abrogate last year's spending deal.

"I'll be working to erase this $14 billion spending increase. It's important," he said. "Otherwise, we are breaching this agreement the first year."

While Sessions is complaining about Democrats wanting to over-spend, Democrats have complained for months about House Republican spending bills that would spend less than the discretionary caps agreed last year, something Republicans say is allowed under the BCA.