The eighth amendment proposed in the Bill of Federalism would increase the power that the President of the United States has for bringing Federal budgets into balance…

Section 1. The budget of the United States shall be deemed unbalanced whenever the total amount of the public debt of the United States at the close of any fiscal year is greater than the total amount of such debt at the close of the preceding fiscal year.
Section 2. Whenever the budget of the United States is unbalanced, the President may, during the next annual session of Congress, separately approve, reduce or disapprove any monetary amounts in any legislation that appropriates or authorizes the appropriation of any money drawn from the Treasury, other than money for the operation of the Congress and judiciary of the United States.
Section 3. Any legislation that the President approves with changes pursuant to the second section of this Article shall become law as modified. The President shall return with objections those portions of the legislation containing reduced or disapproved monetary amounts to the House where such legislation originated, which may then, in the manner prescribed in the seventh section of the first Article of this Constitution, separately reconsider each reduced or disapproved monetary amount.
Section 4. The Congress shall have power to implement this Article by appropriate legislation; and this Article shall take effect on the first day of the next annual session of Congress following its ratification.

This amendment goes beyond the notion of a “line-item veto” and allows the President to reduce or zero out any amount in any legislation (save for the exceptions in section 2) in the year following the passage of an unbalanced budget. Congress does retain its power to restore funding reduced by the President through the usual 2/3 override process.
I would consider modifying this just a bit, allowing the President to reduce amounts until the budget is balanced, but not beyond.
In his commentary on this proposed amendment, Georgetown University Law Professor and Bill of Federalism author Randy Barnett explains the budgeting practices he feels make this amendment necessary…

The practice by Congress of aggregating thousands of lines of expenditures into “omnibus” appropriation bills has greatly diminished the veto power that the Constitution reposes in the President. Because of their reluctance to threaten a government shut down, Presidents are loath to veto such bills. Knowing this, Senators and Representatives can load spending bills with pork, knowing that Congress will never have to give an up or down floor vote to a particular line item and that the threat of a presidential veto is empty. While there is great demand for constitutional requirement of a balanced budget, mechanisms for this that have been devised to date are highly complex, typically contain numerous exceptions and loop-holes, and lack effective means of enforcement. By linking the goal of a balanced budget with a temporary presidential line-item veto, the eighth proposed amendment provides a real incentive for Congress to devise a balance budget; if Congress fails to do so, the President would then have a temporary line item veto power over any appropriation in the budget. For example, should Congress enact a budget with a deficit, the President could veto Congressional earmarks and be held accountable for failing to do so. The amendment also ensures that Congress will retain the same power to override any presidential line item veto as it currently has for a traditional veto.

Links to the earlier proposed amendments are below the fold…

• Article VII: Term limits for Senators and Congressman
• Article VI: States allowed to repeal acts of Congress
• Article V: Reaffirming the freedom of expression
• Article IV: Treaties are not a basis for governing within the US until their provisions are explicitly written to law
• Article III: Limits on unfunded mandates and on conditions applied to Federal disbursements to states
• Article II: Limiting Federal Powers under the Interstate Commerce Clause
• Aritcle I: Reconstituting the Taxing Power of the Federal Government