Murkowski accused the other Democrats of uniting behind the bill to bolster Reid's chances.
Murkowski testily responded that Bryan and other Democrats were irresponsible in trying to combine the two topics.
Murkowski is the daughter of former Gov. Frank Murkowski, whom Palin defeated in the 2006 gubernatorial primary.
Lisa Murkowski, who is running a write-in campaign after losing in the Republican primary to Mr. Miller.
Democrats believe his prospects have improved because Ms. Murkowski and Mr. Miller are splitting the conservative vote.
So in January Mr Murkowski reversed himself and suggested using part of the Permanent Fund to pay state bills.
ECONOMIST: Can the Permanent Fund be used to wipe out the deficit?
Alaska's Governor, Frank Murkowski, has reached a deal with three major oil companies.
Lisa Murkowski (R- Alaska), well-funded by Alaska fishing organizations, has repeatedly tried to tie up the FDA in red tape.
Lisa Murkowski that would prohibit the Environmental Protection Agency (EPA) from regulating greenhouse gas emissions under the Clean Air Act.
In January Republican Governor Frank Murkowski proposed a 5% bed tax on all hotel rooms and cruise ships in Alaskan waters.
The day after Allen's guilty plea, Palin sent e-mails to staffers asking for information on his ties to her predecessor, Frank Murkowski.
CNN: E-mails: Palin moved to tie oil scandal to ousted rival
In the Senate, Frank Murkowski is trying to organise a similar proposal.
The McCain campaign said that Palin had reduced yearly travel expenses by roughly 80 percent of the amount spent by predecessor Frank Murkowski.
Co-sponsors include U.S. Senator Jeff Bingaman (D-NM), U.S. Senator Mark Begich (D-AK), U.S. Senator Lisa Murkowski (R-AK), and U.S. Senator Patty Murray (D-WA).
Alaska's senior senator, Lisa Murkowski, was not happy with Palin's decision.
Lisa Murkowski of Alaska, the top Republican on the energy committee.
Meanwhile, in a scandal that rocked Alaska's political establishment, Palin moved quickly to link a key figure to her defeated predecessor, Frank Murkowski, the documents show.
Governor FRANK MURKOWSKI (Republican, Alaska): While the oil stands independent of the gas, clearly there is a connection, because what the producers basically accepted was a package.
Frank Murkowski, R-Alaska, the senior Republican on the Senate Energy Committee, spoke about the challenges of getting Bush's energy reform package through the Democrat-controlled Senate in the fall.
The panel veered a little from Mr Murkowski's wishes for it by toying with the idea of a state income tax (Alaskans pay no such tax at present).
ECONOMIST: Can the Permanent Fund be used to wipe out the deficit?
Palin had beaten Murkowski in 2006 in a primary battle in which she campaigned as a reformer and backed an unsuccessful 2010 challenge to Murkowski's daughter, U.S. Sen.
CNN: E-mails: Palin moved to tie oil scandal to ousted rival
Last year's twice-failed Disclose Act and the recently introduced Wyden-Murkowski Act aim to reregulate campaign spending by groups whose speech was liberated by the Supreme Court's Citizens United ruling.
Lisa Murkowski, R-Alaska, had been the only one, but was forced to resign her post when she decided to run as a write-in candidate after losing her GOP primary.
CNN: Despite new female faces in Congress, numbers in decline
Praise and criticism followed Palin's ascendance to the governor's office after she won the state Republican primary against incumbent Gov. Frank Murkowski and took the general election in 2006.
Now, with a former oil man in the White House, and energy issues on the front page of the nation's newspapers, Murkowski's bill would open up the refuge for drilling.
After helping Joe Miller beat Lisa Murkowski, the incumbent, in Alaska's Republican primary last month, the Tea Party Express announced that it would match what it had spent in Alaska in Delaware.
Senator Frank Murkowski, who chairs the House committee on Energy and Natural Resources, said the energy secretary made repeatedly given assurances that improved security measures at the lab were protecting America's nuclear secrets.
Lisa Murkowski, the ranking member of the Senate's energy and natural resources committee, said that she continues to support Shell's plans and that the suspension was evidence of the company's commitment to safety.
Many of Mr Murkowski's own proposals for boosting the state economy, such as a plan to increase logging in the Tongass National Forest, require the federal Forest Service to spend millions building new roads.
ECONOMIST: Can the Permanent Fund be used to wipe out the deficit?
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