"I would be surprised if we didn't override her," North Pole Republican Rep. John Coghill said.
An override would require a three-fourths majority in both the House and Senate.
"This is just one of those cases where there is such a profound difference of opinion between the legislative branch of government and the executive branch," said Rep. Mike Hawker, R-Anchorage. "We could have one of those rare and difficult instances where we are actually able to override a governor's veto of an appropriation item."
Palin initially said she would not accept about a third of the $930 million Alaska was eligible for under the American Recovery and Reinvestment Act, citing "strings" that could bind the state to federal mandates and increase the size of government.
As legislators delved into the stimulus plan and found few strings, they passed a bill accepting all federal money.
Palin accepted all the stimulus funds except for the $28.56 million for energy cost relief. Palin said she rejected the stimulus money because it came with a string attached: a requirement to adopt building codes. Lawmakers dispute Palin's assessment.
The money could have helped the Alaska Energy Authority cover priority projects not paid for this year, or furthered the Alaska Housing Finance Corporation's efficiency programs.
This week, Senate President Gary Stevens, House Speaker Mike Chenault and other lawmakers sent a letter to federal Energy Secretary Steven Chu asking to preserve the state's option to accept the money.
They asked if Chu would hold open the application process until legislators reconvene in January and could consider a veto override. They also want to know if the state can still get the money if they override Palin's veto and she still refused to accept the money.
The letter was also signed by Sens. Lyman Hoffman and Bert Stedman, chairmen of the Senate Finance Committee, Reps. Hawker and Bill Stoltze, chairmen of the House Finance Committee, and House Minority Leader Beth Kerttula.
Stevens, who leads the bipartisan majority, said although it appears there are enough votes for an override, he remains hesitant to move forward. He said Palin would apparently end up with the final say on the money regardless.
"I'm not sure there's a point in our overriding the governor's veto because the governor still has the option of not applying for the money," the Kodiak Republican said.
Stevens said he isn't inclined to call a special session, meaning any override vote would have to wait until the next legislative session, in January. They are awaiting word back from Chu.
When asked if Palin would accept the federal money if lawmakers override her veto, spokeswoman Sharon Leighow, in an e-mail, said, "We will cross that bridge when we get there."
She pointed to Palin's comments in a press release issued several weeks ago noting a veto override is an option for the Legislature.
"At this point, we won't speculate on where the votes would fall," Leighow said.
State Sen. Lesil McGuire, R-Anchorage, said legislators should override the veto even if Palin continues to refuse to seek the money from the federal government.
Alaskans, she said, want their representatives to stand up to Palin on this.
"We are the people responsible for carrying out their will and allowing their voices to be heard. So I think there is merit in overturning the veto and having the discussion with (Energy Secretary) Chu to see if there is still a chance," McGuire said.