A new statewide poll by the University of Washington Center for Survey Research found most voters would support a state gay marriage law if it's approved by the Legislature.

Of voters surveyed, 55 percent indicated they would uphold a Legislature-approved same-sex marriage law if it were challenged by referendum. The poll found 38 percent would oppose the law and 7 percent were undecided.

However, additional questions in the poll found that 44 percent of voters surveyed said gays and lesbians should have the same legal right as straight couples to marry; and 22 percent said they should have the same legal rights as married couples, but it should not be called marriage.

Seventeen percent said there should be no legal recognition of gay and lesbian couples. The wide-ranging poll touched on several other issues, including the state budget shortfall.

The Washington Poll surveyed 938 registered voters statewide from Oct. 10-30. It has a plus or minus 3.2 percentage points margin of error.

State Sen. Ed Murray, D-Seattle, and Rep. Jamie Pedersen, D-Seattle, have said they're considering a push for gay marriage in the next regular session in January. Both men have worked on gay rights issues for years and have been building incrementally toward gay marriage.

The Legislature will go into special session on Nov. 28 to deal with about a $2 billion hole in the state's $32.2 billion two-year budget, which runs through June 2013.

The poll found that about 44 percent of those surveyed wanted the shortfall handled entirely or mostly through budget cuts, 39 percent wanted it dealt with through a combination of cuts and tax increases, and 12 percent wanted the shortfall handled entirely or mostly through tax increase.