The House vote to impeach President Donald Trump shifts the action to the Senate, where Minnesota Democrats Amy Klobuchar and Tina Smith have pledged to sit in judgment impartially despite their strong support of the House impeachment inquiry.

Both senators are under pressure to follow the party line, but neither has committed herself to voting to remove the president from office. The issue is likely to be dominant in Smith’s expected tough re-election fight in 2020. And the time demands of the Senate trial could keep Klobuchar off the presidential campaign trail at a critical time.

Under the Constitution and Senate rules, all members must take an oath affirming that they will “do impartial justice according to the Constitution and laws” during the impeachment trial.

“I will go onto the Senate floor and hold up my right hand and swear to deliver impartial judgment,” Smith said in an interview Thursday with The Associated Press, adding she “will not prejudge” without hearing all the evidence.

Klobuchar, a former prosecutor, made a similar commitment after the House vote Wednesday night, which fell mostly along party lines.

“The American people deserve to hear evidence and witness testimony during a full and fair trial in the Senate,” Klobuchar said in a statement. “If the President has any facts to present in his defense to the articles of impeachment, we should hear them. When the Senate convenes for a trial, I will take my oath seriously and carry out my constitutional duty.”

Like Klobuchar, Smith also wants to hear from people close to Trump whom he blocked from testifying. Given that the president is proclaiming his innocence, Smith said, he should want administration officials who have direct knowledge of the issues to come forward.

Smith also said she’s concerned about how fairly Senate Republicans will run the proceedings, given that Majority Leader Mitch McConnell is openly working closely with the White House and has signaled that he intends to conduct a swift trial and acquit the president.

The Senate had been expected to hold the trial next month. But Democratic House Speaker Nancy Pelosi threw uncertainty into the process late Wednesday by refusing to say when she would send the two impeachment articles to the Senate, which can’t open the trial until she does. That uncertainty leaves Klobuchar, and other senators running for president, in a bind with the crucial Iowa caucuses set for Feb. 3 and the New Hampshire primary coming up Feb. 11.

Klobuchar, whose staff said she was not doing interviews Thursday, has said that she’ll just have to figure out how to deal with being off the campaign trail. She said she could use surrogates if necessary, including her husband and daughter, while she’s tied down on Capitol Hill.

“We have no idea how long it should take,” Klobuchar told reporters while campaigning in Henniker, New Hampshire, last month. “It should take as long as is necessary for senators to make their decision, and I just can't predict what the whole procedure will be. I know one thing — that it’s my constitutional duty, I’ll be there. We’ll find a way to campaign around the country.”

Smith’s likely opponent in the 2020 election, former Republican U.S. Rep. Jason Lewis, has already been using impeachment against her.

“It’s incumbent on people like Tina to step up and put a stop to this, but my fear is she won’t, and that’s why I’m in the Senate race,” Lewis said in an interview Thursday.

Lewis, a staunch Trump supporter, called impeachment an “affront” to the 63 million Americans who voted for Trump in 2016 and to the Minnesotans who came within 44,765 votes of giving the state’s 10 electoral votes to Trump. And he said he expects Smith to be “a very partisan player” in the trial.

Smith insisted she won’t.

“In the United States Senate I pledged allegiance to the Constitution, not my political party,” she said. “Minnesotans are sick and tired of the way partisan politics get used as a weapon. I’m not going to do that. ... I think what Minnesotans really care about is whether their senators are working for them.”