(CNN) The Republican-controlled House of Representatives is expected to overwhelmingly approve a bipartisan bill giving Congress the authority to block any effort by President Donald Trump to ease sanctions against Russia.

The vote scheduled for Tuesday comes the same day as the President's son-in-law makes his second appearance in two days before congressional panels investigating charges that Trump campaign associates may have coordinated with Russian officials during the 2016 presidential campaign.

Jared Kushner, a senior adviser to the President, met with staff of the Senate intelligence committee on Monday and said afterward at the White House: "Let me be very clear: I did not collude with Russia, nor do I know of anyone else in the campaign who did so."

The bill includes new sanctions on Russia, Iran and North Korea and also includes a provision that gives Congress veto power if the Trump administration tries to ease sanctions on Russia. The bill was a product of intense negotiations between the two chambers, and a deal was announced Saturday , but it may not be completely sealed just yet.

Senate foreign relations committee Chairman Bob Corker told reporters Monday he still thinks the Senate may make small changes to the North Korean portion of the bill, which was added by the House.

"There may be a few more changes to the bill," Corker said. "Generally speaking, there's no real daylight between us, but when you get down to the final throes members want to weigh in."

Corker would not commit that the bill could get to the President's desk before the House is scheduled to leave town for August recess at the end of the week, but said the two chambers were still working on the procedure so the bill could quickly move back and forth between the House and Senate.

New York Rep. Eliot Engel, the top Democrat on the House foreign affairs committee, said a deal was still in place, but there were concerns something could go wrong before it gets to the President's desk.

"The more stuff you put in it, the more problems you potentially have with it, and I'm keeping my finger on North Korea because I don't know what Corker and the Senate is going to do," Engel said. "In principle I think we're all in agreement with it, even though there's some things I would prefer not to have in the bill, like North Korean sanctions. But I could live with it if that's the price I have to pay to have a bill."

It's unclear whether Trump will sign the bill. In recent weeks, top administration officials have lobbied Congress for changes that would have weakened the role for members of Congress to put the brakes on the executive branch if it works to scale back sanctions on Russia.

Those efforts were rejected by bipartisan negotiators, who instead focused on alleviating concerns from industry and some European allies.

Over the weekend White House Press Secretary Sarah Huckabee Sanders expressed support for the new version, but her boss, White House Communications Director Anthony Scaramucci, wasn't as definitive about its prospects for being enacted.

"You've got to ask President Trump that," Scaramucci said on CNN's State of the Union on Sunday, when asked if the President backed the bipartisan package.

On Monday, when pressed by reporters on the President's position on the current bill, Sanders said: "He's looking over where it stands exactly at this point and we'll keep you guys posted on the decision. I think the important part of this is the President very much supports sanctions on those countries and wants to make sure that those remain, but at the same time wants to make sure that we get a good deal."

Corker said he felt the administration was learning more about what the bill does. "My sense is they're understanding more fully how congressional review works, what it really means, and developing a fuller understanding of that," he said.

In a signal of how much support the bill has House GOP leaders brought the bill up under so-called "suspension" rules that require the legislation pass with a two-thirds majority.

Congressional aides say regardless of whatever action Trump takes, both chambers expect to easily pass the measure with veto-proof two-thirds majorities.

An earlier version was approved by the Senate 98-2, but House GOP leaders raised some procedural concerns with the bill. Several American energy, aerospace, manufacturing and transportation companies also wanted changes to that bill, arguing that several provisions posed problems for business interests in the region being impacted by tougher sanctions in the bill.

Leaders from both the Senate and House expressed support for the revised legislation.

Illinois GOP Rep. Adam Kinzinger said on CNN on Monday that "we expect that the President signs this." Kinzinger said if the President did decide to veto the measure, he has "no doubt" that Congress would override his veto.

In a sign of how partisan the debate on Capitol Hill is over the Russia probe, House Democrats blocked passage of the annual intelligence re-authorization bill, which traditionally passes easily on the House floor. Instead of agreeing to the measure that emerged unanimously from the House Intelligence Committee, Democrats voted against it, arguing the GOP's restricted debate schedule didn't allow them to make changes.

"Given the centrality of intelligence issues this year we didn't think this was the appropriate time to offer this process that doesn't allow members to have input," Rep. Adam Schiff, the top Democrat on the intelligence committee, told CNN.