The first-blush reactions to John Bolton saying he will testify if subpoenaed in a Senate impeachment trial were understandably skeptical. The GOP controls the Senate and has shown no appetite for subpoenaing new witnesses, after all, so it may mean next to nothing.

But even if his Senate testimony may still be a long shot, what about potential testimony in the House?

Experts say Bolton’s decision to say he would abide by a Senate subpoena could undermine any claims he might have to fight a House subpoena. The Democratic-controlled House has thus far declined to subpoena him, but only because he has indicated that he would allow a lengthy court case to play out before appearing, and Democrats said they couldn’t wait.

Now Bolton is signaling, though, that he wouldn’t fight such a subpoena in the Senate.

“Accordingly, since my testimony is once again at issue, I have had to resolve the serious competing issues as best I could, based on careful consideration and study,” the former national security adviser to President Trump said in a statement. “I have concluded that, if the Senate issues a subpoena for my testimony, I am prepared to testify.”

Constitutional scholar Heidi Kitrosser of the University of Minnesota said this could make it much more difficult for Bolton to fight a potential House subpoena.

“By stating that he would testify if the Senate subpoenas him, Bolton has effectively waived any argument against testifying should the House subpoena him,” Kitrosser said. “Bolton had no plausible claim for absolute immunity from showing up to testify in the first place. But even if he previously had such a claim, there is no plausible basis on which it would apply only against a House subpoena and not against a Senate subpoena.”

Bolton is among the most potentially significant witnesses who have yet to testify about the Ukraine scandal. He was perhaps the highest-profile voice of dissent internally, objecting to the “drug deal” that he said Rudolph W. Giuliani was cooking up, according to testimony from Fiona Hill, the White House’s former top Russia adviser. Bolton’s attorney has also said that, as of early November, Bolton knew about “many relevant meetings” that hadn’t been testified to. A person close to Bolton told The Washington Post that the testimony would be damaging to Trump.

Mark Rozell, dean of George Mason University’s Schar School of Policy and Government, agreed there is now “no plausible argument” for Bolton to resist a House subpoena.

“Either he is protected by privilege, or he is not,” Rozell said. “The principle for withholding testimony cannot apply to one chamber but not the other. The whole point of withholding testimony is to protect the privacy of internal White House deliberations or to prevent making public information that could harm the national security.”

Bolton’s argument, though, seems to be that there is simply not enough time in a Senate impeachment trial for the courts to decide on such matters, so he had to make a call on his own.

“It now falls to the Senate to fulfill its constitutional obligation to try impeachments, and it does not appear possible that a final judicial resolution of the still-unanswered constitutional questions can be obtained before the Senate acts,” Bolton said in his statement, right before saying he would abide by the subpoena.

Law professor Lisa Kern Griffin, of Duke University, said Bolton may also try to resist a House subpoena by arguing that the impeachment process has now concluded — something Bolton emphasized in his statement.

“Presumably, Bolton’s grounds for refusing a House subpoena now would be that the House has completed its investigation and hearings and held the vote on articles of impeachment,” Griffin said. “It’s all very well and good to proclaim his willingness to comply with a subpoena that [Majority Leader] Mitch McConnell has insisted the Senate will not issue."

House Democrats have yet to signal that they will subpoena Bolton. In a tweet, House Intelligence Committee Chairman Adam B. Schiff (D-Calif.) suggested this was still a matter for the Senate and said nothing about a House subpoena.

And just because Bolton’s argument against a House subpoena may be damaged now doesn’t mean he would immediately testify. Democrats would have to characterize why they need his testimony, given that Trump is already impeached. And there would still be a legal process if the House subpoenaed him and he opted not to immediately obey it, a process that Democrats have already indicated they aren’t eager to start. There is also the risk that it could undermine their efforts to secure testimony from Donald McGahn, Trump’s former White House counsel.

Aside from the House subpoena issue, the benefit of Bolton’s announcement for Democrats, theoretically, is that it will put pressure on McConnell (R-Ky.) and other GOP senators who could break ranks and insist upon his testimony. Perhaps it looks bad if a witness who knows a lot and says publicly that he’s happy to testify isn’t asked to. McConnell, though, has been perfectly happy to play the bad cop on this stuff, and moderate GOP senators — four of whom would probably need to cross over — have not sent a strong signal that they will push for a robust trial.

Bolton testifying definitely just got more likely, but that doesn’t mean it is likely.