AUGUSTA — Maine lawmakers overturned Republican Gov. Paul LePage’s veto of the $6.7 billion state budget Tuesday as they raced through dozens of remaining bills so they could head home to their districts for the summer.

The Legislature’s rejection of LePage’s budget veto means that the two-year spending plan that cuts taxes for many residents, funds additional drug enforcement agents and maintains state aid for cities and towns will go into effect Wednesday, the start of the fiscal year.

The Democratic-controlled House of Representatives voted 109-37 to approve the budget over the governor’s objections. The Republican-led Senate followed with a 25-10 vote.

With that, lawmakers furiously sorted through a slew of bills still in play and dozens of other vetoes from LePage. They also faced increasing pressure to investigate allegations made by House Speaker Mark Eves, a Democrat, that LePage threatened to withhold more than $500,000 a year from a charter school to get Eves removed as president there.

Just moments after the budget was finalized, more 100 people holding signs that read “impeach the bully” and “unfit to govern” rallied outside the Statehouse. The Legislature’s Government Oversight Committee is expected to convene Wednesday to decide whether the state’s watchdog agency will launch an investigation into the allegation LePage abused his power.

“The allegations, if true, are a direct threat to our Democratic principles,” said Cushing Samp of Saco, who helped organize the rally.

The budget debate revealed deep divisions among House Republicans, as many urged their colleagues to reject the spending plan and fight for deeper tax cuts and more money for services for the elderly and disabled. Others, like House Republican leader Ken Fredette, said that although the budget isn’t perfect, it’s the best deal his party could hope for in divided government.

“This is divided government, folks,” Fredette said. “You don’t get everything you want.”

The two-year budget will cut the top individual income tax rate from 7.95 percent to 7.15 percent and keep the sales tax at 5.5 percent, instead of reverting it back to 5 percent in July. Maine residents will see a net tax cut of $135.4 million in 2017 when all the changes to the tax code are taken into account.

The measure will also pump $80 million more into K-12 education over the two years and double the popular homestead property tax credit program to $20,000. The measure also increases funding for nursing homes by $16 million, eliminates the tax on military pensions, keeps revenue sharing at roughly $62 million a year and funds four new Maine Drug Enforcement Agency positions to help with the state’s anti-drug efforts.

LePage blasted lawmakers in a scathing four-page veto letter Monday and accused them of using the “false threat” of a government shutdown to pass a budget largely devoid of any of the reforms he proposed. He pledged to continue fighting for his priorities of lower taxes and reduced welfare rolls.

“I was elected to stand up for the people of Maine. You are the people of Maine and I’m going to work for you with every ounce of blood and breath I have in my body,” LePage said.

Also Tuesday, the House approved $100 million in bond proposals that would support infrastructure improvements and the construction of more senior housing across Maine. If approved by the Senate, the bond measures will go before voters in November.

Lawmakers gave final approval to other bills, including a measure to allow people to carry concealed handguns without a permit. The bill now heads to LePage, who has threatened to veto every measure that gets to his desk until lawmakers pass his plan to ask voters whether they want to eliminate the income tax. That would mean lawmakers returning in mid-July for another session dedicated to trying to override any vetoes that LePage issues after they finish their work this week.