When Democratic Rep. Brian Higgins resigned to become president of Shea’s Performing Arts Center in Buffalo, his party was relatively optimistic about holding onto his New York district. As NBC News reported, the results of the congressional special election to fill the vacancy suggest Democrats’ optimism was well grounded.

Democrats won a special election for a House seat in western New York on Tuesday, The Associated Press projected, further shrinking the GOP’s narrow majority in the House. Democratic state Sen. Tim Kennedy defeated Republican town supervisor Gary Dickson in the 26th District, a reliably blue area that includes Buffalo and some of its surrounding suburbs.

This wasn’t an instance in which the GOP nominated an unelectable candidate. On the contrary, Dickson was the first Republican elected as town supervisor in the Buffalo suburb of West Seneca in 50 years.

The results were nevertheless lopsided: According to a Buffalo News report, Kennedy, who heavily outspent his GOP rival, defeated Dickson by roughly 37 points.

At first blush, the outcome might not seem to affect the national landscape much. In a reliably Democratic district, voters replaced a former Democratic member with a Democratic state senator. Republicans didn’t make much of an effort to even compete in the contest.

But on Capitol Hill, the results of the race in New York’s 26th district complicate the legislative arithmetic for the beleaguered House Republican majority conference.

When Republican Rep. Mike Gallagher of Wisconsin recently resigned, the GOP majority in the chamber fell to just 217 members. This left GOP leaders with a one-vote margin: On any given vote, if Democrats remained united, Republican measures would fail if just two of the party’s members broke ranks.

Last week, however, Democratic Rep. Donald Payne Jr. of New Jersey died unexpectedly, increasing the number of vacancies, and lowering the threshold to pass legislation in the House to 215. Or put another way, in light of Payne’s passing, the Republicans’ majority margin went from one to two.

The results of the Buffalo-area special election change that arithmetic: After Kennedy is sworn into office, GOP leaders will once again find that their margin in the chamber is back to just one vote.