US President Donald Trump speaks to reporters after a phone conversation with Mexico's President Enrique Pena Nieto on trade in the Oval Office of the White House in Washington, DC on August 27, 2018. - President Donald Trump said Monday the US had reached a "really good deal" with Mexico and talks with Canada would begin shortly on a new regional free trade pact."It's a big day for trade. It's a really good deal for both countries," Trump said."Canada, we will start negotiations shortly. I'll be calling their prime minister very soon," Trump said.US and Mexican negotiators have been working for weeks to iron out differences in order to revise the nearly 25-year old North American Free Trade Agreement, while Canada was waiting to rejoin the negotiations. (Photo by MANDEL NGAN / AFP)        (Photo credit should read MANDEL NGAN/AFP/Getty Images)
PHOTO: Mandel Ngan/AFP/Getty Images
US President Donald Trump speaks to reporters after a phone conversation with Mexico's President Enrique Pena Nieto on trade in the Oval Office of the White House in Washington, DC on August 27, 2018. - President Donald Trump said Monday the US had reached a "really good deal" with Mexico and talks with Canada would begin shortly on a new regional free trade pact."It's a big day for trade. It's a really good deal for both countries," Trump said."Canada, we will start negotiations shortly. I'll be calling their prime minister very soon," Trump said.US and Mexican negotiators have been working for weeks to iron out differences in order to revise the nearly 25-year old North American Free Trade Agreement, while Canada was waiting to rejoin the negotiations. (Photo by MANDEL NGAN / AFP) (Photo credit should read MANDEL NGAN/AFP/Getty Images)
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(CNN) —  

After weathering criticism that it is paying too little attention to the President’s defenders in the House, the White House has been ramping up its outreach to Senate Republicans ahead of a likely trial in the upper chamber in the weeks ahead.

Some White House aides and advisers still think President Donald Trump has resisted forming an adequate team to defend against impeachment, as he’s nixed forming a war room or hiring more staff and lawyers. However, the President and staff have spent more time in the past week reaching out to the senators who will likely decide his fate if the House impeaches him.

Several White House officials said the shift in focus to the Senate, after leaving House Republicans largely to chart their own way through the early days of the inquiry, includes the advice from Senate Majority Leader Mitch McConnell at a meeting last week for Trump to stop insulting Republican senators.

The House voted to formalize impeachment inquiry procedures on Thursday, a historic vote that passed mainly along party lines, though two Democrats broke ranks and joined Republicans in voting against the resolution. The significant step provides the procedural details for how the House will move its impeachment inquiry into its next phase as it investigates a whistleblower complaint alleging that the President attempted to pressure Ukraine to interfere in the 2020 presidential election by investigating the family of his potential political rival, former Vice President Joe Biden. White House officials said Trump monitored Thursday’s impeachment proceedings on the House floor.

Over plates of chicken in the Roosevelt Room on Thursday, the President talked impeachment with a handful of Republican senators just hours after the House voted. Like many White House officials, Trump focused on the pair of Democratic members who bucked leadership, according to Sen. Josh Hawley, one of more than a half-dozen senators who met with Trump at the White House.

A source familiar with Trump’s meeting with senators said the President told the attendees in the room that he was pleased that no Republicans had defected during the vote on the impeachment resolution. Trump also continued to stress the importance of the summary transcript of the Ukraine call released by the White House. The White House’s Ukraine expert, Lt. Col. Alexander Vindman, testified earlier this week that the transcript omitted some details of the call, including by replacing a portion of the conversation where Trump mentioned tapes of Biden with an ellipsis.

Many Republicans and advisers remain deeply frustrated with the way the White House is handling the entire situation. But some point to these signs that the President and his staff may be preparing to handle the second phase of impeachment better than the first, which many even within the White House have acknowledged hasn’t gone well.

One of the reasons for the White House’s Senate outreach is that the President’s team is concerned about reports that the Senate part of the process will not be as predictable as what unfolded in the House.

Still, the source familiar with Thursday’s meeting said it’s unlikely at this point that many GOP senators will break from the President.

“If I had to bet any money, I would say only one at this point,” the source said. “Sen. Mitt Romney.”

A separate GOP official aware of discussions among Senate Republicans was much more careful about making predictions, saying, “It’s too early to tell.”

This official said some GOP senators remain concerned about the President’s actions and are awaiting for the facts to come in.