By Richard Cowan

WASHINGTON (Reuters) - The Republican Party's two-year run in the majority of the U.S. Senate is at serious risk and may well end on Nov. 8, senior congressional aides said on Wednesday, blaming Donald Trump as a drag on down-ballot Republican candidates.

With 13 days to go before elections, several Senate aides from both parties privately warned of trouble for Republicans.

"Things are not good ... the Senate is gone," said one Republican aide who asked not to be identified in order to candidly discuss the turbulent outlook for the 2016 campaign.

Citing opinion polling, the aide said Republicans could lose Senate seats in six battleground states: Pennsylvania, Illinois, Wisconsin, New Hampshire, North Carolina and Missouri.

A Reuters/Ipsos poll released on Wednesday and conducted from Oct. 20 to Oct. 24 found that 41 percent of Republicans now expect Clinton to win the election, versus 40 percent for Trump.

That is a sharp decline in confidence from last month, when 58 percent of Republicans said they thought their party's nominee would win, versus 23 percent for Clinton.

Republicans now hold 54 of the Senate's 100 seats. Democrats must snatch four seats to win a majority, provided their presidential candidate, Hillary Clinton, beats Trump. That would make Clinton's running mate, Tim Kaine, the tie-breaking Senate vote since the vice president votes in order to break a tie.

On Tuesday, the nonpartisan Cook Political Report predicted Democrats would gain five to seven seats. Such a result would leave them short of the 60 votes needed to easily get things done in the Senate, but it would provide a majority.

A less pessimistic Senate Republican aide said Senate control still "could go either way" but sketched out problems.

In Pennsylvania, the aide said, Senator Pat Toomey has to "fight off dead weight at the top of the ticket," referring to Trump. In Missouri, he said, Democrat Jason Kander, who is trying to unseat Senator Roy Blunt, is "a great candidate."

Nationally, "the reason we don't hold the Senate, if we don't, is because of Donald Trump," the aide said.

Of course, this has been a volatile and unpredictable year, and there is still time for trends to reverse. Democrats stressed they are not breaking out the champagne.

According to RealClear Politics, Toomey leads by 1.8 percentage points in Pennsylvania while Blunt is up by a point in strongly Republican Missouri and Senator Richard Burr has a 2.8-point lead in North Carolina over his Democratic challenger.

Still, a senior Senate Democratic aide said, "We have a lot more paths to a majority than they do."

Republicans entered the 2016 Senate races at a disadvantage, having to defend 24 seats to only 10 for Democrats.

Democratic President Barack Obama, who is still relatively popular, won at least one of his two White House races in most of the states where Republicans currently are struggling, such as New Hampshire, Pennsylvania and Nevada.

Clinton leads Trump by about 5 points in some national polls. Studies show a pattern of voting in recent decades in which the outcome of Senate races has had a significant correlation to who wins the White House.

Polling in the hardest-fought states points to extremely close races with Republican incumbents' backs against the wall.

In New Hampshire, Republican incumbent Kelly Ayotte is in a tough race with her Democratic challenger, Governor Maggie Hassan. University of New Hampshire political science professor Dante Scala said Republican senators in that state and Pennsylvania face the "one-two punch" of independent voters potentially being turned off by Trump and an electorate that leans Democratic in presidential election years like 2016.

"Given the overall environment, it tilts to Hassan," Scala said.

(Editing by Kevin Drawbaugh and Jonathan Oatis)