Our Daily Digest is a lunchtime look at the stories we have our eyes on at the Capitol and beyond. Here’s what we are watching today:

The nation’s highest court is hearing arguments on the constitutionality of same-sex marriage bans today, in a case with major implications here in Texas. They are hearing from attorneys on both sides about whether same-sex couples should be allowed to be married. The court’s ruling would set a nationwide precedent, including here in Texas, one of 13 states where same-sex marriages are still illegal. A court challenge against Texas’s ban is currently held up in the Fifth Circuit Court of Appeals in New Orleans, but those judges are expected to wait for the Supreme Court to rule.

The full Texas House chamber gave initial approval to its $4.9 billion tax cut plan today, voting 141-0 in favor of the bill. House Bill 31 would cut the the state sales tax, and is expected to save the average family of four $172 per year. The current state sales tax rate in the state is 6.25%, not including any extra taxes established by counties. That would fall to 5.95% under Rep. Dennis Bonnen’s proposal. It’s a drastically different approach than the Senate plan, which focuses on property tax cuts, and has become a major line in the sand between the two chambers this session. They’re also expected to debate House Bill 32, which cuts the margins tax paid by businesses. The Senate plan also includes a so-called franchise tax cut, an item Governor Abbott demanded by veto threat at the beginning of the session. Opponents of the tax cut plans say the money is better spent on things like roads or education funding.

In other news, leadership from both chambers met for the first time today to try to come to a compromise on the budget. The conference committee on House Bill 1 met for about 30 minutes today with the Legislative Budget Board as they try to work out their differences. And a House committee heard testimony today on plans to legalize medicinal marijuana in Texas. The proposal would legalize marijuana for treatment of chronic illnesses like PTSD and epilepsy, and would set up a licensing system for growers and dispensaries.

Tonight on “Capital Tonight,” Chuck Smith with Equality Texas will evaluate what the attorneys and justices had to say in the Supreme Court today. Plus, political strategists Harold Cook and Ted Delisi will give their takes on the week’s headlines at the State Capitol. Tune in to Time Warner Cable News at 7 p.m. and 11 p.m.