Connecticut lawmakers began the new legislative session in January with a weighty to-do list. With adjournment just days away, some of the key items on that list remain unfinished.

Chief among them is a new, two-year state budget.

Democratic House Speaker Joe Aresimowicz of Berlin said he's hopeful a "handshake deal" reached last week between Democratic legislative leaders and Democratic Gov. Ned Lamont will come up for a vote Monday. The General Assembly's regular session adjourns at midnight on Wednesday, although lawmakers might pass a resolution to extend the deadline.

Some other major issues, including electronic tolls and recreational marijuana legalization, will likely have to wait until a special legislative session or possibly longer.

Here's a look at where things stand in the final days:

THE BUDGET

Lamont and the Democrats announced on May 30 they had reached an agreement on a roughly $40 billion, two-year tax and spending plan they say closes a projected two-year, $3.7 billion gap.

While some details have been revealed — Lamont said the plan doesn't include a capital gains tax increase or higher personal income tax rates — as of Saturday, rank-and-file lawmakers still had not met with their leaders to go over the finer points, including how much state aid their cities and towns can expect.

Aresimowicz acknowledged Saturday that "it's taking a lot longer" than expected to actually transform the framework into budget documents. The deal was reached without the Republicans, the minority party in the General Assembly. He said he was hopeful all lawmakers will be able to get more information over the weekend.

Some parts of the deal are receiving last-minute pushback, including a proposal that would impose income taxes on certain limited liability companies that don't pay the corporation tax. Proponents say taxing these so-called "pass-through" entities will impact wealthy business owners, a claim contested by business groups.

"Most small business are middle-income earners, and the vast majority of their businesses happen to be structured as pass-throughs," said Andrew Markowski, state director of the National Federation of Independent Business in Connecticut. "So, any increase in this tax impacts them in a very negative way because they make plans based on their predicted costs."

PAID FAMILY MEDICAL LEAVE

Both the Democratic House of Representatives and Senate have now passed legislation that would create a paid family medical leave system in the state, funded by a 0.5 percent payroll tax on most Connecticut workers.

They now need to pass separate legislation that addresses some concerns raised by Lamont, who has threatened to veto the bill if the changes aren't made.

The compromise gives the governor more control over the program's oversight board, which he originally criticized as too unwieldy. It slightly reduces its size and makes changes Lamont said will allow the estimated $400 million program to operate more nimbly.

Republican Senate Leader Len Fasano, of North Haven, insists the agreement Lamont reached with the Democratic legislative leaders "does nothing to change the damaging problems" with the bill Lamont originally raised.

ELECTRONIC TOLLS

While Lamont had urged lawmakers to pass a tolling bill before the regular session adjourns, days after urging the General Assembly to focus on the budget, it appears likely the contentious issue will be addressed in a special session.

Aresimowicz last week said it was "highly unlikely" there would be a vote, given the anticipated lengthy debate.

Lamont has released a working draft of a 24-page transportation bill he said provides a "solid foundation from which to build upon" during the special session. It calls for no more than 50 tolling gantries on Interstates 84, 91, 95 and parts of Route 15 and the creation of a new Connecticut Transportation Commission, which would be charged with setting toll rates during peak and off-peak times and for different types of vehicles.

MARIJUANA, GAMBLING AND VACCINES

The fate of three major issues this session — the legalization of marijuana, the expansion of gambling and the elimination of a religious exemption from vaccines for schoolchildren — likely will need extra time.

The vaccine issue has been put on hold until the Department of Public Health provides lawmakers with advice on how to handle such a change. On the subject of marijuana, there are mixed opinions about whether a bill might come up in the final days or possibly during a special session. The issue is a complicated one, especially given interest among some lawmakers to link the legislation to erasure of certain criminal records.

And while Lamont's efforts to reach a deal on a wide-ranging gambling bill stalled, Aresimowicz has been hoping to reach a last-minute agreement.