Arriving in the final few weeks before an election, that kind of money can pay for television advertising and get-out-the-vote operations that have the potential to tip the closest races. At the very least, it will help narrow the financial disparity that has given the Democratic Party an advantage. And it could not come at a more urgent time for Republicans.

A half-dozen Republican strategists working on races across the country this week said that they had noticed a consistent uptick in their candidates’ poll numbers in their most recent surveys, most notably in several of the tightest Senate races. Speaking anonymously to divulge private campaign data, they all said the best-case situation was that they were seeing the kind of consolidation among Republican-leaning voters that has eluded the party for most of the year.

That movement, which they attribute to the unifying effect of the confirmation fight over Justice Brett M. Kavanaugh, has been occurring in states where the Democrat had been either tied with or ahead of the Republican — including Arizona, Missouri, Montana, Nevada and West Virginia.

Republicans are less optimistic about holding onto the 23 seats they need to keep their majority in the House. But strategists now believe that if the bounce they are seeing in their internal numbers holds, they can considerably limit their losses.

Still, this last-minute infusion of cash from the Adelsons to the Congressional Leadership Fund and the Senate Leadership Fund, both of which have close ties to party leaders in Congress, is not a panacea. President Trump’s unpopularity is a drag on Republican candidates in many of the most competitive House districts, especially those with more affluent and well-educated electorates. And advertising rates have been skyrocketing in the final weeks before Election Day, meaning that $20 million can buy only a fraction of what it could have a few months ago when the Adelsons gave their initial donations.