Gov. Andrew Cuomo and lawmakers in New York State are tantalizingly close to making political history by enacting a campaign-finance reform law that not only would weaken the power of special interests and make elections more competitive, but also could set an example for the rest of the country.

In January, Mr. Cuomo announced an excellent package of campaign reforms. At the top of the list was the long-sought goal of public financing of political candidates. The package is part of his 2014-15 budget proposal; the budget must be approved by the end of March.

Public campaign financing has already worked well in New York City. It would give state voters something they seldom have — a real choice of candidates on Election Day — by providing public matching funds for smaller contributions. This change would encourage people who aren’t rich to enter the contest for public office.

The prospect of greater competition is the reason many in Albany have tried to stop public financing. But encouragingly, in the last few days the Assembly included the governor’s campaign finance proposal in its version of the budget. The problem, as is often the case in Albany, is the Senate, controlled jointly by Dean Skelos, the Republican leader, and Jeffrey Klein, an independent Democrat. Mr. Klein has long supported public financing. Mr. Skelos has been publicly opposed to taxpayer financing. A full Senate verdict is expected this week.