The group of House centrists will soon introduce a bill capping discretionary spending at specific levels. The move would challenge their leadership and the president, who are balancing concerns with the nearly $1.6 trillion deficit in 2010 with those who say government spending on job creation is the way out of the recession.

The spending levels sought by the Blue Dogs may result in spending cuts, which would go beyond Obama’s proposal to save $250 billion over the next decade by freezing non-security discretionary spending for three years, said Rep. Baron Hill (D-Ind.), a senior Blue Dog.

“Two hundred and fifty billion is a lot of savings with a freeze on discretionary spending, but I think we can do better,” Hill said in a brief interview.