Returning from Congress’s Memorial Day recess on Monday, senators are sounding increasingly optimistic that a bill aimed at sanctioning Russia and its allies will receive a vote on the floor by the end of the month. Lawmakers say that the escalation with the Russian Federation will only put President Trump in a stronger negotiating position. 

In late May, Senators Graham and Blumenthal unveiled a list of 79 other senators who would be backing their sanctions legislation — a rare feat in a chronically divided Congress. If enacted, the bill would allow the president to impose sanctions on dozens of government and non-government officials, as well as impose 500 percent tariffs on countries that do business with Russia. 

Mr. Blumenthal told reporters Monday that, based on his conversations with his colleagues, he expects the sanctions bill to receive a vote before the Senate goes on another week-long vacation at the end of June. 

“We think in the coming weeks we see a vote on the floor,” Mr. Blumenthal said, referencing comments made by Speaker Johnson on Monday that he supports the legislation. “The White House is somewhat supportive, which I think is one of the reasons [for] Speaker Johnson’s comment today, which was pretty positive.”

The Connecticut Democrat said he and Mr. Graham planned to iron out some changes to the bill with the White House, though he would not disclose what those changes would entail. 

As he was leaving the Capitol on Monday, the majority leader, Senator Thune, confirmed to the Sun that he was in consultation with the White House while working to get the bill to the floor. 

“We’re in conversations with the White House about that,” Mr. Thune said. 

Another co-sponsor of the bill, Senator Tillis, told the Sun Monday that he hopes the president realizes that this sanctions bill would just be an additional weapon in his arsenal that he could use at his own discretion. He says the president would be wise to understand that such a tool would be helpful as negotiations between the United States, Russia, and Ukraine seem to be stalling. 

“I’d vote for that bill every single day. I hope that the administration will see that it’s a real enabler for them now that Putin’s true nature has really been exposed to the president,” Mr. Tillis said. 

The White House did not immediately respond to a request for comment. 

Mr. Trump has grown increasingly frustrated with both President Putin and President Zelensky in recent weeks, as peace talks stall and even a cease-fire seems out of reach for the time being. 

The president spoke with both the Russian and Ukrainian leaders in May, and stated that Mr. Putin was ready to make a deal. Mr. Zelensky later said publicly that he was ready to lay down weapons and begin talks. 

The negotiations have seemingly gone nowhere, however. The Ukrainians even launched a daring attack against the Russian military inside the country’s borders just over the weekend. On Sunday, Ukraine said it launched more than 100 drones and destroyed dozens of Russian aircraft.