It's called the "No Taxpayer Subsidies for Political Campaigns Act," and it would defund the Clean Elections Act, which was approved by voters in 1998.

Local Arizona Senator Steve Pierce authored SCR 1025, a bill which is brief and to the point:

Be it resolved by the Senate of the State of Arizona, the House of Representatives concurring:
1. Article VII, Constitution of Arizona, is proposed to be amended by adding section 19 as follows if approved by the voters and on proclamation of the Governor:
19. Taxpayer money to candidate or campaign for statewide office or legislature prohibited: definitions
Section 19. A. Taxpayer money shall not be used to fund any political candidate or campaign for statewide office or the office orf member of the legislature.
B. For the purposes of this section:
1. "Statewide office" means Governor, Secretary of State, State Treasurer, Attorney General, Superintendent of Public Instruction, Corporation Commissioner, Mine Inspector or any nonfederal office elected by a vote of the qualified electors of this state as a whole.
2. "Taxpayer money" includes:
(a) Any tax, fee, assessment, surcharge, forfeiture, penalty, fine, other revenue or monies collected by this state, a political subdivision, department, agency or instrumentality of this state or a city or town.
(b) Any contribution, donation or expenditure that is eligible for a state tax reduction, deduction, exemption, exclusion, credit, donation, checkoff or other tax feature.
2. The Secretary of State shall submit this proposition to the votgers at the next general election as provided by article XXI, Constitution of Arizona.

When asked about the legislation, which passed the Senate at the end of February, and is now being considered by the House, Pierce replied succinctly, "My bill is to ban public funding of elections. We can use the money for border security."

Because the Clean Elections Act was voter-approved, any legislative changes to it must also be approved by the voters.

The Supreme Court Also Takes a Close Look at the Clean Elections Act

However, the voters have no say when it comes to Supreme Court scrutiny, which will happen next week when arguments against matching funds will be heard.

A provision of Arizona's Clean Elections Act provides that besides the funds a candidate automatically gets when they agree to run "clean," that same candidate will also get matching funds if a "traditional" opponent raises more than an arbritrary amount, thus supposedly evening out their resources.

In August of 2008, the Institute for Justice and the Goldwater Institute filed challenges to the law, claiming that the matching funds aspect of the Clean Elections Act stifles free speech.

Here is a brief video these two organizations use to explain explain how Arizona's law works:

The Supreme Court evidently thought the challenge had merit; last June, the Court put an injunction on matching funds right in the middle of the campaign for several statewide offices. (See the Goldwater press release here.) Several candidates that expected to receive additional funds, found their campaigns strongly curtailed by the Court's action.

The Goldwater Institute, in a press release sent out today, noted, "Although these cases raise questions that are vitally important to the right of Arizonans to speak freely about politics, they directly raise a larger national issue as well: Does the First Amendment permit the government to drive private spending from our political campaigns by burdening the speech of independent groups and candidates who refuse to take government money? Ultimately, government funding of campaigns means government control over campaign speech. Under our Constitution, though, it is the public—not the government—that decides whose political message is worth supporting."