(Adds Trump statement in paragraph 6)
WASHINGTON, June 6 (Reuters) - President Donald Trump will huddle with congressional leaders on Tuesday, seeking to rev up a stalled legislative agenda as the summer break draws closer and a probe into Russian meddling in the 2016 election campaign grinds on.
Elected pledging to overhaul the healthcare system and slash taxes, Trump has yet to notch a major legislative win, and time is running out before lawmakers leave Washington for August.
The White House is trying to spur momentum this week by highlighting policy plans - a task made more difficult with the spotlight on testimony by James Comey, the FBI director fired last month by Trump, to the Senate Intelligence Committee on Thursday.
Comey will be grilled by senators on whether Trump tried to get him to back off an investigation into alleged ties between the president's 2016 campaign and Russia. Trump denies any collusion with Russia, and has called the investigation a "witch hunt."
The White House wants to see Senate Republicans vote on healthcare reform legislation before they leave for a break in August, Marc Short, Trump's top aide on Capitol Hill, told reporters on Monday. The House of Representatives passed a bill in May.
"Big meeting today with Republican leadership concerning Tax Cuts and Healthcare. We are all pushing hard - must get it right!" Trump said in a statement on Twitter early on Tuesday.
Also on tap before the break:
A vote to raise the government's borrowing authority, known as the debt limit, should also take place before the break, Short said.
Republican fiscal conservatives routinely demand budget cuts and other concessions as a price for raising the debt limit, setting up a likely fight.
Congress will then turn its focus to overhauling the tax code in September. While the administration would prefer that the effort not add to the national debt, Short stressed that the top priority would be cutting taxes.
"We want it to be revenue neutral, and we are still supportive of tax reform, but I am also saying to you that what we believe is most important to get the economy going is the tax cuts," he said.
The Trump administration has outlined a broad plan that would cut tax rates for businesses and streamline the tax system for individuals. But, the proposal has been short on details -- including the cost of the tax cuts and what loopholes would be closed.
The healthcare bill passed by the House could result in 23 million people losing insurance, the Congressional Budget Office estimated, though Republicans have challenged that conclusion. The bill would also reduce federal deficits by $119 billion between 2017 and 2026, according to the analysis.
Short said he believed that the Senate healthcare bill would be "similar" to the House package.
Senator John Cornyn, the No.2 Republican in the Senate, said Monday evening he thought there would be a vote on a healthcare bill in the Senate in July. (Additional reporting Richard Cowan, Susan Cornwell, Roberta Rampton and Susan Heavey; Editing by Lisa Shumaker & Simon Cameron-Moore)