This week’s rhetoric over the budget — or lack thereof, yet — showcases a messaging war over the blame game between the two ends of Pennsylvania Avenue.

First, Speaker John A. Boehner repeatedly tried to pin the automatic sequester cuts on President Barack Obama in a Monday floor speech. Now, Obama’s Democratic allies in the House are trying to pin rampant deficits on Congress.

The back-and-forth underscores that in the House this week, it’s all about messaging, with Republicans bringing a bill to the House floor to force Obama to submit a balanced budget that by all indications is destined never to become law.

An amendment introduced by freshman Rep. Mark Takano to the GOP’s budget bill would subtly alter the legislation’s findings section, which currently says, “Since taking office, the President has allowed the Federal debt to grow by nearly $6 trillion and total debt now exceeds the size of the entire economy of the United States.”

The amendment by the California Democrat would change that text to read that “Since the President took office, Congress has allowed” the deficit to rise.

The House Rules Committee allowed Takano’s amendment to be considered but not one submitted by Rep. Chris Van Hollen, ranking member on the Budget Committee and a top strategist for Democrats on spending battles.

The Maryland Democrat’s amendment would temporarily replace the sequester cuts with a combination of spending cuts and tax increases.

Specifically, the amendment eliminates certain “direct payment” farm subsidies, increases taxes on the oil and gas sector, and implements the “Buffett rule” proposal to ensure high-income individuals pay a minimum tax rate.

Van Hollen estimated the replacement provisions were about one-third cuts and two-thirds new revenues.