The Assembly approved sweeping climate-change legislation Tuesday that extends the state’s targets for reducing greenhouse gases from 2020 to 2030 in a controversial bill that saw White House officials and Gov. Jerry Brown privately urging lawmakers for support.

Under SB32, the state would reduce its greenhouse gas emissions to 40 percent below 1990 levels by 2030. The bill would piggyback on AB32, the California Global Warming Solutions Act of 2006, which calls for California to reduce greenhouse gases to 1990 levels by 2020. The state is expected to reach that target.

But one of the state’s programs to fight climate change — cap and trade — remains threatened by a legal challenge that has cast uncertainty on its future and has discouraged the carbon credit market. And, on Tuesday, officials revealed that the latest auction, once again, fell short of their hopes.

SB32, which the Senate has already passed, heads back to that body, which is expected to pass the amended legislation before the Legislature’s deadline next Wednesday. Brown said in a statement that he will sign the bill when it reaches his desk, and he expressed optimism about the future despite the threats to the cap-and-trade program.

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The auction occurred last week before the fate of SB32 was known. But the passage of SB32 will not eliminate doubts as to the program’s future, according to Michael Wara, an associate professor at Stanford Law School.

Although SB32 passed, “it didn’t pass by a two-thirds majority, which is highly significant from a legal perspective,” he said. That’s because a two-thirds majority is required for the Legislature to approve a tax. Whether the revenue from the Air Resources Board’s quarterly auctions constitute a tax is being questioned in a legal challenge from the California Chamber of Commerce.