The House on Saturday was heading toward passage of a $95 billion foreign aid package for Ukraine, Israel and Taiwan, as Speaker Mike Johnson put his job on the line to advance the long-stalled legislation in defiance of hard-liners from his own party.

Lawmakers were expected on Saturday afternoon to vote separately on aid for Ukraine, Israel and Taiwan, as well as on another bill that includes a measure that could result in a nationwide ban of TikTok and new sanctions on Iran. The fourth bill was meant to sweeten the deal for conservatives.

Mr. Johnson structured the measures, which will be melded into one after each piece is approved, to capture different coalitions of support without allowing opposition to any one element to sink the whole deal. Each of the aid bills for the three nations is expected to pass overwhelmingly, and the Senate is expected to take up the legislation quickly and send it to President Biden’s desk, capping its tortured path to enactment.

The legislation includes $60 billion for Kyiv; $26 billion for Israel and humanitarian aid for civilians in conflict zones, including Gaza; and $8 billion for the Indo-Pacific region. It would direct the president to seek repayment from the Ukrainian government of $10 billion in economic assistance, a stipulation supported by former President Donald J. Trump, who has pushed for any aid to Ukraine to be in the form of a loan. But the legislation also would allow the president to forgive those loans starting in 2026.

The scene that is expected to play out on the House floor on Saturday will reflect both the broad bipartisan support in Congress for continuing to help the Ukrainian military beat back Russian forces, and the extraordinary political risk taken by Mr. Johnson to defy the anti-interventionist wing of his party who had blocked the measure for months. In the end, the speaker, himself an ultraconservative who had previously voted against funding Ukraine’s war effort, circumvented his right flank and was relying on Democrats to push the measure through.

For months, it was uncertain whether Congress would approve another round of funding for Ukraine, even as the momentum of the war in Ukraine shifted in Russia’s favor. Republicans dug in against another aid package for Kyiv unless President Biden agreed to stringent anti-immigration measures, and then refused to take up legislation that paired the aid with stiffer border enforcement provisions.

But after the Senate passed its own $95 billion emergency aid legislation for Ukraine, Israel and Taiwan, Mr. Johnson began — first privately and then loudly — proclaiming that he would ensure the U.S. would “do our job” and send aid to Kyiv, sticking to his vow even in the face of an ouster threat from the right wing.

Warning that President Vladimir V. Putin of Russia could send forces to the Balkans and Poland if Ukraine were to fall, Mr. Johnson said he had made the decision to advance aid to Kyiv because he “would rather send bullets to Ukraine than American boys.”

“My son is going to begin at the Naval Academy this fall,” Mr. Johnson told reporters at the Capitol earlier this week. “This is a live-fire exercise for me as it is for so many American families. This is not a game. It’s not a joke. We can’t play politics on this. We have to do the right thing, and I’m going to allow an opportunity for every single member of the House to vote their conscience and their will.”

His decision infuriated the ultraconservative Republicans who accused Mr. Johnson of reneging on his promise not to advance foreign aid without first securing sweeping policy concessions on the southern border. On Friday, a third Republican, Representative Paul Gosar of Arizona, announced his support for ousting Mr. Johnson from the speakership over the move.

“I’m concerned that the speaker’s cut a deal with the Democrats to fund foreign wars rather than secure our border,” Representative Thomas Massie, Republican of Kentucky, said on Friday as he argued against a procedural measure to bring up the package, which needed the votes of Democrats to be approved.

Mr. Massie has been one of the most vocal opponents of the foreign aid legislation, and has joined the bid to oust Mr. Johnson because of it.

The Republican opposition to the measure — both on the House floor and in the critical Rules Committee — forced Mr. Johnson to rely on Democrats to get it to the floor, for which they did a critical test vote on Friday.

“Democrats, once again, will be the adults in the room, and I’m so glad Republicans finally realize the gravity of the situation and the urgency with which we must act,” said Representative Jim McGovern of Massachusetts, the top Democrat on the Rules Committee. “But you don’t get an award around here for doing your damn job.”

One of the bills to be considered Saturday would help pave the way to selling off frozen Russian sovereign assets in order to help fund the Ukrainian war effort. American allies, including France and Germany, have been skeptical about the viability of such a move under international law, and have instead been pushing to give the proceeds on the interest from the nearly $300 billion of frozen Russian assets directly to Ukraine, either in the form of loans or as collateral to borrow money.

The bill would also impose sanctions on Iranian and Russian officials and further limit the export of U.S. technology used to make Iranian drones.

Lawmakers also are expected to vote on a series of amendments, including a pair proposed by Republicans that would zero out or limit funding for Ukraine. Those efforts are expected to fail.

Alan Rappeport contributed reporting.