Providence Mayor Brett Smiley’s administration is one step closer to getting legislative approval to raise the city’s tax levy by more than 7 percent, but there are still two state senators who are going to have a major say over how the city’s legislative agenda takes shape over the next month.

The House of Representatives overwhelmingly approved a bill last night that allows the city to exceed the state’s 4 percent cap on tax levy increases, a proposal Smiley says is largely necessary because of the city’s settlement last year to increase funding for the school department.

That bill still needs Senate approval, and the two senators to watch are newly elected Majority Leader Frank Ciccone and Senator Jake Bissaillon.

Ciccone and Bissaillon are both viewed as supporters of Smiley, but their neighborhoods are poised to see some of the largest property tax increases, which they fear will substantially drive up rents for their constituents.

Start with the obvious: Ciccone is suddenly much more powerful than he was three months ago. As majority leader, he likely has the ability to singlehandedly push through or kill Smiley’s tax bill.

As Channel 12’s Alexandra Leslie reported on Tuesday, the Smiley administration is warning that not passing the tax levy bill could result in massive layoffs and other cuts in the city. With state leaders facing their own budget challenges, the last thing they want is a Providence budget crisis that, in some ways, the Senate would be creating.

Then again, Ciccone doesn’t want to be a one-term majority leader (unless he gets a promotion). A vote for the levy increase could add to the likelihood that he’ll face a challenger in the Democratic primary next year.

Bissaillon’s bet: Bissaillon has been much more direct with the Smiley administration: He maintains that he won’t support a tax levy increase unless it agrees to an obscure tax change related to industrial properties in the city – his argument is that he doesn’t want properties like the Manchester Street Power Station to see a tax decrease when his constituents are going to see large increases.

In some ways, Smiley’s team took Bissaillon for granted. They were dismissive of his proposal, and assumed he’d be a good team player and support their levy increase anyway. But he has made it clear that he isn’t bluffing, and the administration has indicated it will support a version of his bill.

“I won’t support it unless I feel like I’ve done everything I can to help my constituents,” Bissaillon said Tuesday.

What to watch: The tax levy bill isn’t the only one the Smiley administration is seeking. Lawmakers seem poised to support an event parking tax that could help the city, and there appears to be momentum on a new tax breaklargely aimed at the “Superman” building.

This story first appeared in Rhode Map, our free newsletter about Rhode Island that also contains information about local events, links to interesting stories, and more. If you’d like to receive it via e-mail Monday through Friday, you can sign up here.

Dan McGowan can be reached at dan.mcgowan@globe.com. Follow him @danmcgowan.

EXETER — Dan Cummings, Nick Cote, Marcos Uben and Noah Roberts won the 4×400 relay (3:30.55) while Roberts finished first in the 800 (1:58) for the Westerly boys at Saturday’s Class C outdoor track and field championships at Exeter-West Greenwich High School. Uben also finished second in the 110 hurdles (15.39) and 300 hurdles (40.87) and Jack Speranza took second in the shot put (46-4) as the Bulldogs were fifth overall (56 points). St. Raphael Academy was the team champion (166 points).