Republican Members from Texas can breathe a sigh of relief — for now.

Gov. Rick Perry (R) agreed late Tuesday afternoon to take up redistricting in a special legislative session, and the proposed Congressional map appears to be aimed at keeping every incumbent in office, with the exception of Rep. Lloyd Doggett (D).

“I think this map is a great starting point and it is positive that the House and Senate redistricting chairmen joined together and put forth a public map,” Rep. Joe Barton (R-Texas) said in a statement Tuesday.

The proposal includes four new House seats, bumping up the delegation to 36 Members. Texas is adding more House seats than any other state, and Texas Republicans are taking advantage by drawing two of the districts in the heavily GOP areas around Fort Worth and Houston and by including more Republicans in Doggett’s district.

The other two proposed districts are in heavily Hispanic areas that are likely to vote for Democrats — one in south Texas and another that stretches from Austin to San Antonio. Doggett could opt to run in the latter district, but it would still be an uphill climb for the Democrat, given that he would likely have a primary challenge. Some high-profile Hispanic officeholders from that area have already expressed interest in running for Congress.

“I’m ready to live in a Winnebago if that’s what it takes,” Doggett told the Austin Chronicle on Tuesday. “But I think it’s still a little early. This map is a long way from reality. Much of its design is to convince people there’s nothing we can do about it, and there still is.”

The new map would also shore up some freshman Republicans’ districts, building on gains the GOP made last cycle when the party won three Democrat-held seats. For example, the proposed map would shift GOP Rep. Blake Farenthold’s district to the north, leaving many of its Hispanic voters in one of the newly drawn districts.

Texas state lawmakers had seemed unlikely to pass a map before the legislative session was scheduled to end Monday evening, and Perry insisted that he would not call a special session just so lawmakers could debate Congressional redistricting. But a last-minute standoff Monday night over a school finance issue pushed the Legislature into overtime, and Perry called the Legislature in for a special session Tuesday morning that, under Texas law, could last up to a month if necessary.

State House and Senate leaders of the redistricting committees presented the map without fanfare Tuesday morning, and Perry put redistricting on the agenda by that evening. The move buys state lawmakers more time to pass a map. If they do not, a three-judge panel would decide the delegation’s fate, an alternative that Texas Members openly bemoan.

“Now open debate can begin and I am glad that the governor added congressional redistricting to the special session’s agenda so the legislature can complete its job,” Barton said in his statement. “I have always believed — and still do — that this process is better solved in the State Capitol and not in a courtroom.”

Any Congressional map passed in Texas must get final clearance from the Justice Department, which will determine whether it adheres to the Voting Rights Act.