Republican senators say they're not worried that President Trump's much-criticized performance at his summit meeting with Russian President Vladimir Putin will hurt Republicans in the midterm elections in November, and are predicting that the event will be forgotten by then.

"I don't think it's the kind of foreign policy issue that has a lot of long-term resonance with voters, and might not even have much short-term resonance with voters," Sen. Roy Blunt, R-Mo, told the Washington Examiner. "You've got to assume that the president will bring up many things between now and then that will send people on a different direction."

"I think people are quickly ready to move onto other things. If there's one lesson to be learned from Donald Trump, it's how quickly people are willing to move onto whatever comes next," Blunt added. "There may be things that last from here 'til November, but I wouldn't think this kind of foreign policy discussion would be one of them."

[Related: Republicans overwhelmingly back Trump's performance at Putin summit: Poll]

Issues like Russia and North Korea have become major news stories over the last few months, but neither have turned into a major campaign subject. Republicans and Democrats are mostly talking about the economy, and Republicans believe they can keep the conversation there or on other topics that benefit them.

"I think what matters is how somebody's going to vote on the Supreme Court justice. I think what's going to matter is how they're going to embrace economic policies that cut taxes," said Sen. Cory Gardner, R-Colo., chairman of the National Republican Senatorial Committee. "They're going to ask questions about whether they support ideas Democrats have to abolish ICE."

"When you're voting in November, you're going to be voting on those issues," Gardner added.

Democrats admit that pocketbook issues will play best as the election approaches, but are still pushing to keep Trump's questionable behavior with Putin on voters' minds.

"The first thing on people's minds are pocketbook issues," said Sen. Chris Van Hollen, D-Md., chairman of the Democratic Senatorial Campaign Committee. "This is why it's so important to have an independent-minded senator who is going to hold the president accountable on some of these issues."

"I think [Helsinki] is going to have greater lasting impact," Van Hollen added.

Sen. Bill Nelson, D-Fla., a top target among Republicans to defeat in the fall, said Helsinki could remain a problem for Republicans if Trump "continues to act strangely."

During his press conference with Putin, Trump downplayed the idea that Russia hacked into Democratic servers, and later said he misspoke and that he believes Russia was to blame. But Trump's backtracking only seemed to solidify the position of partisan voters.

According to an Axios poll, 79 percent of Republicans approved of how Trump handled the press conference with Putin. However, 62 percent of independents disapproved.

[Also read: Most disapprove of Trump's Putin summit, but nearly half of Republicans doubt Russia meddled: Poll]