House Democratic leaders are seeking to reassure members of the moderate to conservative Blue Dog Coalition that they are finally committed to following the pay-as-you-go budgeting rules they have sometimes flouted despite enshrining them in House rules.

As a signal of their intent to get serious on the matter, Speaker Nancy Pelosi (D-Calif.) and House Majority Leader Steny Hoyer (D-Md.) on Tuesday are sending budget conferees a letter stating they will not take up four major bills — addressing middle-income tax cuts, the estate tax, the alternative minimum tax and Medicare reimbursement rates — unless they are fully paid for, or include a provision giving PAYGO the force of law, or if such a measure has already passed.

“Under those three circumstances, we’ll consider legislation. If one of those three criteria is not met, we won’t be considering that legislation on the floor,— Hoyer told reporters Tuesday. “The Speaker and I will be making that clear to our own Members, and to members of the Conference and to the other body.—

Those stipulations are already laid out in the budget conference report, but because the blueprint lacks the force of law, Blue Dogs are worried the Senate could simply ignore the orders. It is not yet clear whether the letter from House Democratic leaders will assuage the 51-member bloc of fiscal conservatives. They are set to meet Tuesday night to discuss it.

Rep. Baron Hill (D-Ind.), a Blue Dog co-chairman, on Tuesday introduced a bill to force PAYGO into law.

“Hoosier families have to live within a balanced budget, and so too should Congress,— Hill said in a statement. “And, Congress should have to strictly adhere to PAYGO, thus transforming PAYGO rules to having the force of the law behind it. The President’s support of this measure is much appreciated and a huge bolster of efforts to make sure we do not leave our children and grandchildren with massive debt.—