There are two ways of disciplining the United States Senate and the President for failing to negotiate with the House of Representatives to produce a budget: one is political and the other is constitutional.
The political solution is to vote for different members of the Senate and a different President. You will notice that I have not suggested replacing your member of Congress, regardless of party affiliation. The reason for that is that the US House of Representatives has passed a budget and forwarded it to the Senate every year of Republican control since that party regained the Senate; but the Senate has failed to do likewise. In addition, the President since taking office in 2009, has consistently failed to obey federal law requiring a timely, date-certain, proposal of a budget. You could, of course, vote for a different representative, but that would apply electoral discipline to a member of the one House of Congress that has not, at least technically, been derelict in its duty.
The constitutional solutions include at least two approaches.
One is much discussed recently as a result of the publication of "The Liberty Amendments," by constitutional lawyer and radio host, Mark Levin. That approach is for the States -- in sufficient number -- call for a convention for proposing amendments to the Constitution. Such a convention could make changes to the Constitution in the nature of your proposed limitations on benefits for failure of duty. That approach is outlined in the Constitution, Article V: "The Congress, whenever two thirds of both houses shall deem it necessary, shall propose amendments to this Constitution, or, on the application of the legislatures of two thirds of the several states, shall call a convention for proposing amendments, which, in either case, shall be valid to all intents and purposes, as part of this Constitution, when ratified by the legislatures of three fourths of the several states, or by conventions in three fourths thereof, as the one or the other mode of ratification may be proposed by the Congress; provided that no amendment which may be made prior to the year one thousand eight hundred and eight shall in any manner affect the first and fourth clauses in the ninth section of the first article; and that no state, without its consent, shall be deprived of its equal suffrage in the Senate."
The other is for the balance of powers to do its work, if it will and can. The Congress has the law-making power. The President has the executive power. The Supreme Court and the lower federal courts have the judicial power. These powers were divided in order to guard against a rising tyranny in our country. But, guarding against tyranny isn't the only effect of depositing law enforcement and adjudicatory powers outside the Congress (the Congress being both House and Senate). That reason is that the laws of the United States may still be applied against those that enact them. If Senators or Congressmen do engage in unlawful conduct (accepting bribes, committing extortion), then that second constitutional discipline of prosecution and punishment may discipline the individual wrong-doer.
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Have a read at the machinations of Congress during the revolutionary war, or frankly any period since....nothing new here .....
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The problem with imposing punishment for failure to agree is that it is unclear who to blame that failure on. Surely you do not mean that a senator can be punished because others refuse to vote his way, or that he can be punished for refusing to vote for a bill he does not agree with. No individual senator has the power to pass a bill on his own. Basically, your options are impeachment (very unlikely and difficult) or voting out at next election. Impeachment would work if someone has actually bought votes, but I think you probably have no proof of that. A one term limit would require a constitutional amendment, but is possible. It is hard for me to see how that would lead to greater levels of agreement among senators.
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