WASHINGTON (REUTERS) - After an acrimonious year where they failed to agree on almost anything, President Barack Obama will host Republican Speaker John Boehner for a rare one-on-one meeting on Tuesday, the White House said.

But with fiscal crises out of the way for the time being, and prospects for major legislation dimming ahead of November midterm elections, it's unclear what the two men will talk about.

Boehner spokesman Brendan Buck said Obama reached out to Boehner with the invitation, and that a "broad set of topics"would be discussed.

"The President and the Speaker are looking forward to discussing a range of items on the legislative agenda," White House spokesman Josh Earnest said.

The two leaders last met alone in the Oval Office on Dec 17, 2012, Buck said. That was during the days of the looming "fiscal cliff," when the two leaders sought but ultimately failed to find a "grand bargain" on tax reform and spending cuts during deficit reduction talks.

"Really? That long ago!" said Larry Sabato, director of the University of Virginia's Centre for Politics, noting that Obama has probably met more often with Russian President Vladimir Putin than with Boehner.

"There are two really different cold wars being waged,"Sabato said.

Since Boehner took the speaker's gavel in 2011, the two leaders have had a near-constant battle over fiscal issues, fights punctuated by a showdown over raising the debt ceiling in 2011, a "fiscal cliff" deadline in late 2012, and a 16-day government shutdown in October 2013.

After the 2012 talks flopped, Boehner said he had given up on negotiating with Obama.

The Republican Speaker has been in the Oval Office a few times since with Senate leaders and House Democratic Leader Nancy Pelosi, and visited the White House once during the October shutdown with a group of House Republican leaders.

Obama and Boehner also sporadically speak on the phone, according to reports from the White House.

But personal contacts have been few and far between.

Although the two men share a passion for golf, they have not hit the greens together since a lone outing in 2011.

There are no more fiscal fights looming in the short term.

Congress agreed to a two-year budget deal at the end of last year, and passed a one-year extension of the debt ceiling earlier this month.

Tuesday's meeting comes a week before Obama delivers his latest budget proposal to Congress, a document that will no longer include an offer to Republicans to trim Social Security benefits in exchange for a deal to overhaul tax breaks for corporations and the wealthy.

Both parties have scaled back their legislative ambitions this year ahead of midterm elections in November, when Democratic control of the Senate is at stake and Boehner's Republicans seek to make bigger inroads in the House of Representatives.

Obama has urged the House to pass a sweeping overhaul of immigration laws, a bill that already has passed in the Senate.

But Boehner has hinted that is unlikely to happen soon.

"A meeting can't change the fundamentals of a midterm election year," the University of Virginia's Sabato said. "These two are on very different paths."