The deals, given to the Legislature in the waning hours of the session last month, were rejected by Democratic leaders of both houses, who said more study is needed before a legislative vote.
But in a letter to Democratic leaders of the Senate and Assembly, Senate GOP leader Dick Ackerman and Assembly GOP leader George Plescia said the compacts "are too important to our state's economic well-being and the prosperity of communities across California to wait until the Legislature reconvenes (next year)."
The GOP leaders said they also want to address woes afflicting California's horse-racing industry.
A spokesman for Schwarzenegger, who also has the power to reconvene lawmakers, said Saturday the governor has ruled nothing out.
Administration spokesman Darrel Ng declined to comment on the letter but said Schwarzenegger wants the half-dozen compacts signed as soon as possible. "Should the governor decide to recall the Legislature, he will make an announcement," Ng said.
Opponents said they were outraged that lawmakers could be recalled to consider the issue. "Does this (GOP) letter truly represent the soul of the California Republican Party? If so, it appears one of our two major political parties has sold its soul for gambling money," said Fred Jones, an attorney for the California Coalition Against Gambling Expansion.
The governor had hoped the pacts would allow him to tout their boost to government revenue during his gubernatorial campaign against Democratic challenger Phil Angelides.
But the deals were blocked by Democratic majority leaders, who refused to act without more in-depth scrutiny.
Repeated attempts to reach Senate leader Don Perata, D-Oakland, were unsuccessful Saturday. Assembly leader Fabian Nu¤ez, D-Los Angeles, also could not be reached immediately for comment.
Administration officials have dismissed Democratic leaders' claims that the pacts were given to the Legislature at the last minute and have hinted at a special session by saying they would press for action anyway.
Republican lawmakers accused Democrats of serving labor groups that want Indian gaming casino workers unionized - an assertion discounted by Perata.
Schwarzenegger, who once opposed unlimited expansion of gambling on American Indian lands, has signed deals with several tribes that would allow them to install tens of thousands of new slot machines.
The latest of the state gambling compacts included agreements that would allow the Sycuan Band of the Kumeyaay Nation to install up to 3,000 new slot machines at its El Cajon casino and resort, and the Yurok Tribe to install the first 99 slot machines on its reservation in Humboldt and Del Norte counties.
The administration previously announced deals allowing three other tribes to increase the number of slots they operate from 2,000 to 7,500 each.