In a session dominated by a gaping state budget deficit, legislators have little more than a month before a May 18 adjournment to resolve that issue and other business before them. A dose of help in the form of federal stimulus money isn't likely to temper the tone or ease the pressure. A look at some of the issues and where they stand:

BUDGET

What's happened: The DFL-controlled Legislature and Republican Gov. Tim Pawlenty still face a $4.6 billion hole in the 2010-11 budget and, so far, there's no agreement on how to fix it. Pawlenty's approach inflicts the least short-term pain but would leave the largest longer-run problems. He would cut $1.3 billion in spending, borrow $1 billion through the sale of long-term bonds and temporarily shift $1.3 billion by delaying state payments to schools. He also would tap the state's Health Care Access Fund for $700 million. That makes for $3 billion in one-time money, not counting $800 million in federal stimulus funds, another one-time solution.

The House would cut less, shift more, and raise $1.5 billion in taxes, while the Senate would cut more than anyone -- $1.5 billion -- avoid shifts and raise a whopping $2.2 billion through higher taxes.

What's next: Pawlenty has said no tax increase will get his signature. House Republicans have pledged to back him up and have the votes (barely) to sustain a veto. Finding a compromise will be difficult.

TAXES

What's happened: DFLers say tax cuts in years past have tilted the system in favor of the wealthy, who now pay a smaller percentage of their income in taxes than the middle class does. No one has committed to any specific tax increases, but the House has persistently raised the idea of a fourth-tier income tax rate that would kick in at $250,000 adjusted gross income for single filers and $500,000 for joint filers.

What's next: Both bodies say they will present the nuts and bolts of their plans this month. The timing will give DFLers just weeks to somehow build public support and round up enough votes to override a certain veto.

BONDING

What's happened: Pawlenty has signaled an interest in working with DFL leaders in producing a bonding bill, a borrowing measure that funds construction and other capital improvement projects. Some Republicans have raised concerns that this is not the time to put more debt on the state's credit card.

The House has passed a $200 million bill; the Senate version is $329 million.

What's next: Reconciling the two versions will be one of the first things legislators turn to when they return from their Easter/Passover break on Tuesday. Pawlenty has said he feels relatively comfortable with a $200 million ceiling.

ELECTIONS

What's happened: The U.S. Senate recount has provided a daily reminder that Minnesota's election laws need work. Secretary of State Mark Ritchie unveiled a fistful of reforms in February, including an effort to simplify absentee voting, a major focus of the recount involving Al Franken and Norm Coleman. Most of Ritchie's proposals have cleared initial legislative hurdles. Republicans, meanwhile, have had little luck pushing their own idea -- requiring voters to show photo IDs at the polls -- but a leading House Republican vows to bring up the issue on the floor.

What's next: There are rumblings that not all of Ritchie's proposals are necessary, but each day the recount drags on provides favorable political wind for the measures.

HEALTH CARE

What's happened: A target for Republicans even in good times, health and human services is under fire from all sides this year.

What's next: Medical Assistance, a federal-state program for the poor, would survive largely intact because federal stimulus funds require it, but that could result in a bigger hit to state-funded programs.

K-12 EDUCATION

What's happened: Schools know things are bad when DFLers aren't proposing an education funding bump. Last week, the Senate passed a 3 percent spending cut for 2010-11 in the basic K-12 formula. A House bill would freeze school spending. Pawlenty proposes modest increases, mostly to high-performing schools and districts that want to shift to alternative teacher pay plans.

What's next: The House bill is to go before the House K-12 Finance Division this week.

LEGACY AMENDMENT

What's happened: Voters passed a constitutional amendment last fall that increases the sales tax to dedicate money for the outdoors, water resources, the arts, and parks and trails. What the money pays for in the first year needs to be approved by Pawlenty and legislators in the next month. Outdoors groups and clean water advocates in particular are hoping that a list of projects they are recommending is adopted "as it is." The Lessard Outdoor Heritage Council, whose members were chosen by the governor and legislators, has recommended $69 million worth of outdoors-related projects.

What's next: Amendment supporters are worried how much legislators will change the recommendations, and even more concerned that Pawlenty and the Legislature will try to use the new money to fill holes left by budget cuts. That would trigger a major political fight.

MEDICAL MARIJUANA

What's happened: A pair of bills would establish a system under which qualified patients could obtain marijuana to ease pain and other symptoms.

What's next: Prospects for passage are perhaps as strong as they've ever been, but Pawlenty is a wild card; his spokesman has said he opposes such legislation but might reconsider if law enforcement does. Supporters hope either to override a veto (less likely) or to change the bill to put the issue on the ballot as a constitutional amendment (becoming more likely).

SAME-SEX MARRIAGE

What's happened: Bills on both sides of the issue have been sitting quietly in the Legislature, going nowhere. Opponents of gay marriage propose a state constitutional amendment stating that marriage is between a man and a woman. On the other side are two measures: One would recognize same-sex marriage, the other would recognize same-sex marriages only from other states.

What's next: With Iowa and Vermont legalizing same-sex marriage, the issue may rise to the forefront in the final days of the legislative session.

VIKINGS STADIUM

What's happened: With their Metrodome lease expiring after the 2011 season, the Minnesota Vikings once again are seeking public aid for a new stadium.

What's next: Even though it faces overwhelming odds, a new Vikings stadium never seems completely off the table at the Capitol.

Staff writers Mark Brunswick, Patricia Lopez, Mike Kaszuba and Norm Draper contributed to this report.