The General Assembly begins 2010 with the Democratic majority and Republican Gov. M. Jodi Rell in a stalemate over how to close an estimated $500 million gap in this year’s budget.

Sound familiar? That’s how they ended 2009.

The price of their inability to put the state’s finances on solid footing last year is that they now face a menu of unpalatable options in an election year: raising taxes, cutting programs and risking the wrath of credit-rating agencies by starving an underfunded pension fund.

Last year, the legislature increased the tax rate from 5 percent to 6 percent on taxable incomes over $1 million for joint filers, $800,000 for heads of households and $500,000 for single filers. It also increased the cigarette tax from $2 to $3 per pack.

Any tax increase adopted this year may have to touch a broader base than the ranks of the wealthy, hitting a greater portion of the electorate.

Everything legislators do in the session that begins Feb. 3 will be measured against how it might play with voters next fall, when all 151 House and 36 Senate seats are up for re-election. Rell is opting for retirement over another term.

In its understated introduction to a primer of the state budget process, the non-partisan Office of Fiscal Analysis observed, “The budget process can undergo great strains during an election year.”

If the solution to their problem is elusive, the cause is clear: a precipitous decline in revenue from the state’s two major sources of tax revenues, the sales and personal income taxes. Income tax has declined faster than the national average.

Sales tax revenue is down 9 percent over the previous year. With 59,000 jobs lost in the past year in Connecticut, revenue from the income tax is down 12 percent, despite the higher rate on top incomes.

The declining revenues automatically triggered the cancellation of a reduction in the sale tax from 6 percent to 5.5 percent that would have occurred Jan. 1.

In November, Rell proposed $337 million in spending cuts that would have reduced local aid by $84 million and taken $52 million from dedicated funds, breaking a commitment to annually provide $10 million for stem cell research. Services for the poor also would have been cut.

Instead, Democrats passed a plan in December to cut $12 million and raise $76 million by rolling back a scheduled reduction in the estate tax. Rell vetoed the bills, calling them insufficient.

Democrats theoretically hold veto-proof majorities in both chambers: 114 of 151 seats in the House, where 101 is the magic number, and 24 of 36 in the Senate, exactly enough for an override.

The estate tax did not receive enough votes in either chamber to override a veto – four votes shy in the House and two votes in the Senate. The $12 million in cuts did have enough support in the House to overcome a veto with 101 votes. But the Senate Democrats, who are not close to a working supermajority on fiscal issues, could only manage 19 votes.

Four Democrats — Gayle S. Slossberg of Milford, Joan V. Hartley of Waterbury, Andrew M. Maynard of Stonington and Robert Duff of Norwalk — voted no. A fifth, Eileen Daily of Westbrook, was absent.

Compounding the legislature’s fiscal challenge is the looming presence of bigger problems in the next two fiscal years. The Office of Fiscal Analysis projected in November that the budget gap for 2011 and 2012 could total $3.8 billion.

Those numbers are likely to encourage some legislators to either join Rell in retirement or run for an office without responsibility for raising taxes or cutting spending.

Rep. Cameron Staples, D-New Haven, co-chair of the tax-writing finance committee, is exploring a run for attorney general. After only one year as House majority leader, Denise Merrill of Mansfield has decided to run for secretary of the state.

Until last year, she was co-chair of the Appropriations Committee and is considered one of the most knowledgeable legislators on budgeting.