PHOENIX - Challengers to the state's open primary system want another two hours to argue in court there are not enough valid signatures to put the measure on the ballot.

Attorney Mike Liburdi told the Arizona Supreme Court on Tuesday he was "cut off" on Thursday by Maricopa County Superior Court Judge John Rea in the middle of his arguments. He said Rea refused to give him more time even after initiative supporters finished early.

"Given the magnitude of the controversy - a proposed constitutional amendment that will fundamentally change the manner in which public officers are elected - it was unreasonable and an abuse of discretion not to provide (challengers) with more time to present their case," Liburdi argued to the high court.

But attorney Kim Demarchi, who represents those pushing the measure, which Rea ruled Friday can go on the ballot, told the justices there is no reason for further hearings. And she said if the process was rushed, they share in the blame.

"The plaintiffs were aware of the limited time that would be available to consider their claims when they filed their lawsuit one week before ballot printing began," Demarchi wrote.

She also said challengers knew exactly how many of the petitions they were challenging as valid based on claims that the circulators, as convicted felons, were ineligible, and they agreed to the half-day hearing.

"Even though they knew they had limited time, they did not use that time efficiently," she wrote.

The high court is under a deadline of sorts to act, as well before the general elections in November.

Maricopa County sent the ballots to the printer last week, but Elections Director Karen Osborne said the presses will not start running until the end of this coming week.

Liburdi claims to have evidence that petitions with more than 7,000 names submitted to the Secretary of State's Office are invalid; But Rea, after hearing the evidence Liburdi was able to present within the time allotted, struck just 2,056 names.

That difference is important if voters are to have a chance to decide whether to get rid of the current system of partisan primaries in favor of having all candidates for any particular office face off in the same primary election, with the top two advancing to the general election regardless of party affiliation.

Based on a 5 percent random sample, Secretary of State Ken Bennett had ruled that circulators did not submit enough valid signatures to qualify for the November ballot.

Demarchi, in her own lawsuit, convinced Rea to rule that 577 from that sample were valid despite conclusions from Maricopa County election officials to the contrary. Under the formula used to verify petition signatures, that was enough to push the initiative over the 259,213 necessary, even with the ones already disqualified due to illegal circulators.

But Liburdi believes that if he has enough time, he could show another 4,000 also should be disqualified, again putting the tally below the threshold and keep it off the ballot.

He said it should not matter that the judge limited presentations prior to the hearing, particularly since part of the elongated presentation was due to the fact "the court required that we introduce our petition signature sheets piecemeal rather than all at once as we wanted to do."