(CNN)Washington is once again awaiting House Speaker Nancy Pelosi's next chess move as she returns to Capitol Hill on Tuesday, continuing to withhold the articles of impeachment from the US Senate while attempting to place another check on President Donald Trump to address his actions on Iran.

With her impeachment strategy to withhold the articles looking wiser -- after former national security adviser John Bolton said Monday that he was prepared to testify in a Senate trial -- Pelosi enters the week facing a new array of pressures.

It was unclear why Bolton decided to speak up when he did, but the development clearly strengthened Pelosi's hand by increasing the pressure on Senate Majority Leader Mitch McConnell to allow witnesses to be part of Senate's impeachment trial.

    She is still trying to balance the desires of her caucus to hold Trump accountable in the midst of an election year, while keeping the heat on the White House at a time when administration officials are navigating a perilous national security situation following Trump's decision to carry out the targeted killing of Iranian commander Qasem Soleimani.

    "I'm sure she's hearing from some in her caucus who are urging her to go very carefully given what's happened," said Democratic strategist Jim Manley. "I'm also entirely confident she's also hearing from a bunch of folks in her caucus who want this done sooner rather than later -- to get it out of the way."

    "She's always been a big believer in the walk and chew gum theory of legislation -- that has always been her mantra," added Manley, who worked for more than two decades in the Senate as an aide to former Massachusetts Sen. Ted Kennedy and former Sen. Harry Reid of Nevada, who served as both minority and majority leader. "So I think she believes they need to finish up the impeachment process while considering the very serious consequences of what the President has unleashed."

    Balancing impeachment fight with response on Iran

    Despite the tenuous international situation with Iran, Pelosi showed no intention of backing away from her criticism of Trump on Monday. When Bolton announced that he is prepared to testify in the Senate impeachment trial if he is subpoenaed, she tweeted that "the President & Sen. McConnell have run out of excuses."

    "They must allow key witnesses to testify, and produce the documents Trump has blocked, so Americans can see the facts for themselves," Pelosi tweeted. "The Senate cannot be complicit in the President's cover-up."

    McConnell's calculations on how to respond to Bolton will likely hinge on the positioning of several swing state senators and sometime critics of Trump, including Sen. Mitt Romney of Utah who told CNN's Manu Raju Monday that "of course" he'd like to hear what Bolton has to say.

    "It turns out, as many of us have known for years, Speaker Pelosi is a very able strategist, perhaps the best there is in Washington at this point in time," said Jen Psaki, who served as White House Communications Director under President Barack Obama and is a CNN contributor.

    "It didn't mean that her risky move" -- in withholding the articles of impeachment from the Senate -- "would result in Bolton coming out and saying he would testify. But certainly she understands how leverage works and how pressure works," Psaki said. "And now she's positioned the argument over whether there should be witnesses to be more in the Democrats' favor."

    Iran drives another stake into the heart of the nuclear deal

    Pelosi was also unsparing in her criticism of the White House on the international front this weekend even at this volatile point in US-Iran relations. In a letter to Democratic colleagues Sunday night, she announced that the House of Representatives would introduce and vote on a War Powers Resolution intended to limit the President's actions in Iran.

    She described the operation that killed Soleimani on Friday at Baghdad International Airport as "a provocative and disproportionate military airstrike targeting high-level Iranian military officials."

    "This action endangered our service members, diplomats and others by risking a serious escalation of tensions with Iran," Pelosi wrote in the letter. "As Members of Congress, our first responsibility is to keep the American people safe. For this reason, we are concerned that the administration took this action without the consultation of Congress and without respect for Congress's war powers granted to it by the Constitution."

    She announced that Rep. Elissa Slotkin, a Michigan Democrat and former CIA and Department of Defense analyst who specialized in Shia militias, would lead the House resolution. The resolution, Pelosi said, would mandate "that if no further Congressional action is taken, the administration's military hostilities with regard to Iran cease within 30 days."

    McConnell and Trump ready to spar with Pelosi

    As the House speaker embarks on that effort to build support for the resolution, she is still locked in a standoff with McConnell, who scoffed at her decision to withhold the articles of impeachment from the Senate late last year -- questioning what leverage she had and accusing her last Friday of attempting to "hand design the trial proceedings," which he called a "non-starter."

    Pelosi stunned Washington moments after the House moved to impeach Trump by stating she did not know when she would send the articles of impeachment over to the Senate, because she wanted assurances that the trial would be fair.

    She subsequently rebuked McConnell as a "rogue leader," chiding with him for collaborating so closely with the White House on impeachment strategy. (Pelosi has supported Minority Leader Chuck Schumer's request to McConnell to subpoena four witnesses, which the Majority leader has so far dismissed).

    In a statement on Friday, Pelosi again called on McConnell to hold a fair trial, stating that he had given notice that he would "feebly comply with President Trump's cover-up of his abuses of power and be an accomplice to that cover-up."

    "Leader McConnell is doubling down on his violation of his oath, even after the exposure of new, deeply incriminating documents this week which provide further evidence of what we know: President Trump abused the power of his office for personal, political gain," Pelosi said in that statement. "The American people deserve the truth. Every Senator now faces a choice: to be loyal to the President or the Constitution."

    In remarks on the Senate floor Monday, McConnell underscored that he believes the question of witnesses must be dealt with later in the trial.

    "The Senate has a unanimous bipartisan precedent for when to handle mid-trial questions such as witnesses: in the middle of the trial," McConnell said, referring to the process for determining witnesses during the impeachment of then-President Bill Clinton.

    He rebuked Pelosi by name when criticizing the Democrats "unseriousness," noting that she is "sitting on the articles she claimed were so very urgent."

    "She's delayed this so the architects of the failed House process can reach over into the Senate and dictate our process as well," McConnell said. "House Democrats are treating impeachment like a political toy—like a political toy, treating their own effort to remove our commander-in-chief like a frivolous game."

    Trump also weighed in Monday on Pelosi's decision to withhold the articles of impeachment from the Senate during an interview with Rush Limbaugh: "I think what they're trying to do is affect the election, illegally, but that's what they're trying to do. The reason they're not sending them is because they're a joke. They are not crimes. There's nothing there."

      It remains unclear what the parameters of the trial will look like, but new evidence continued to trickle out over the winter break about the President decision to withhold aid from Ukraine. And Bolton's announcement Monday could alter McConnell's calculus on witnesses.

      "I'm not so sure I knew what (Pelosi's) strategy was going into this, but it sure looks to be a brilliant move right about now," said Manley after Bolton's announcement Monday.