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The first peek at the politics of the next legislative session is gestating in San Antonio and points west, where an election on Tuesday will decide who’ll be filling Democrat Carlos Uresti’s seat in the Texas Senate.

It’s one piece of the leadership puzzle that will fully take shape in January, when the Legislature convenes in Austin for its regular session. Most eyes have been on who will replace Speaker Joe Straus, and what that might mean for the direction of the Texas House of Representatives.

But the Senate’s operations depend on the Senate’s makeup — and that’s subject to voter review in the elections this week and in November. The upper chamber could be in for some change, too.

Uresti was convicted of 11 felonies including money laundering and fraud and resigned from the Senate in June. He was sentenced to 12 years in prison and ordered to pay $6.3 million in restitution but is appealing his case.

The special election to replace him has been honed down to a runoff — to be settled tomorrow — that will put either a Democrat, Pete Gallego, or a Republican, Pete Flores, in his seat.

Democrats are outnumbered 20-11 in the Texas Senate. Senate rules make it virtually impossible for them to prevail on partisan issues, as it takes three-fifths of the senators — 19 — to bring most issues up for debate. Read that from the Republican point of view: With 20 votes, they have effective control of everything that gets debated.

For the Republicans, winning the SD-19 race would provide insurance in a year when at least two seats held by Republicans are at risk. As the Trib’s Alex Samuels has reported, Sens. Konni Burton of Colleyville and Don Huffines of Dallas face serious challenges in this year’s elections and Sen. Joan Huffman of Houston is only a little better off.

A bad day for the GOP in November could upset that 20-11 advantage, giving Democrats a sometimes veto of legislation they don’t like and forcing what has been a very conservative Senate to moderate.

The House has been historically conservative itself — but hasn’t stuck with the Senate on culture-war issues like last year’s bathroom bill. Additional Democrats in the Senate would be no consolation to social conservatives but might reduce the tensions between that body and the House.

That faction would rather keep the Senate they’ve got and try to get a speaker they like better than Straus, who they blame for getting in the way of some of their pet issues.

A win in San Antonio would help the Republicans. Democrats certainly want to keep the seat. And if the Democrats win — in the first round of voting, Gallego and other Democratic candidates collected almost 60 percent of the votes — they’ll have a foundation for a possible swing in control of the Senate in November.

That November election will figure heavily into the leadership on the other end of the State Capitol, too. It’s where the voters will choose the people who will start the legislative session by electing a successor to Straus.

Republicans have a safe majority — to the extent that anything in politics is safe — in the House, with 95 representatives to the Democrats’ 55. Most of the close November races for House seats find Republicans in defensive positions and Democrats should be able to pick up at least a handful of seats.

Even a five-seat shift in the majority could change the tenor of the speaker race, increasing the bargaining power of the Democrats in a decision that, in some measure, amounts to whether the House is more or less conservative than it is today.

It depends on what voters decide in a small number of elections on the House side and the Senate side. For a couple of sessions, Texans have been witness to a political sibling rivalry between the two legislative chambers. The only way to change that is to make the Senate a little more like the House, or the House a little more like the Senate.

It could go either way.