Senate Budget Committee Chairman Kent Conrad (D-N.D.) is one of two Democrats warning House Republicans not to cut too deeply in House budget. (Manuel Balce Ceneta/AP)

The letter comes as both parties jockey in advance of the scheduled release Tuesday of a budget plan authored by House Budget Chairman Paul Ryan (R-Wis.)

In the letter, Senate Budget Chairman Kent Conrad (D-N.D.) and Senate Appropriations Chairman Daniel Inouye (D-Hawaii) say cutting spending more deeply than agreed to in the summer’s Budget Control Act would mean betraying that difficult deal and would result in a delayed appropriations process for the year.

“We believe that ignoring the BCA represents a breach of faith that will make it more difficult to negotiate future agreements,” they wrote in the letter addressed to House Speaker John A. Boehner and House Majority Leader Eric Cantor (R-Va.).

“Rather than trying to tear down the BCA, we should be holding it up as an example of what can be accomplished if we are willing to set aside our differences and work hard to find bipartisan solutions to our nation’s challenges,” they continue.

Boehner spokesman Michael Steel responded to the letter: “Writing a budget would be a better use of Senate Democrats’ time than writing letters.  Look, with all due respect to Chairmen Conrad and Inouye, the Budget Control Act did not set spending ‘levels’ – it set spending ‘caps’ or ‘limits.’  And, frankly, differences between the Houses on spending would be much easier to resolve if their own Democratic Leadership in the Senate would let them pass a budget for the first time in nearly three years.”

A consensus has been emerging in recent days among Republican leaders that the budget should call for $1.028 trillion in discretionary spending in fiscal 2013, the same level embraced by House conservatives for the 2013 year in Ryan’s budget a year ago.

Under the assumption that House Democrats will oppose the budget resolution because of its proposal to dramatically reshape Medicare and Medicaid, Ryan will need support from conservatives eager to slash spending as deeply as possible to win votes from wary spending hawks and get his plan out of the House.

But the number is $19 billion beneath a spending cap for the year agreed to in difficult summer negotiations over raising the debt deal. The higher $1.047 trillion would cement a spending path that would trim $900 billion from discretionary spending over the 10 years, as agreed to in the debt ceiling deal.

The letter from Conrad and Inouye echoes a warning from Senate Majority Leader Harry M. Reid (D-Nev.) last week, which made clear that Democrats will paint a Ryan budget that spends less than the $1.047 trillion as breaking a deal crafted just seven months ago.

Republicans have insisted that the debt deal set spending caps, and urging cutting more deeply would not undermine the agreement. They want to use the budget to lay out their philosophical commitment to reducing deficits and say Democrats have little room to talk: The Senate has not adopted a competing budget of its own in three years.

But some Republicans on the House Appropriations Committee, tasked with translating the broad budget into spending priorities for agencies and programs, have been quietly urging their leadership to stick with the $1.047 trillion spending level.

An extended clash over how much to spend for the year, they believe, could interfere with their attempts to craft compromises over how much to spend on different agencies.

If House and Senate appropriators cannot reach agreement on spending measures by Sept. 30, a government shutdown would be possible — just weeks before the fall election.

This post has been updated since it was first published.