Texas Lt. Gov. David Dewhurst (R) filed paperwork Tuesday to run for the state’s open Senate seat, and he enters the race as the prohibitive frontrunner to replace retiring Sen. Kay Bailey Hutchison (R).

A source says Dewhurst has sent a video to 500 key GOP activists outlining his platform and beginning his campaign by signing the “Cut, Cap and Balance” pledge on the federal budget.

Dewhurst has long been the 800-pound gorilla in the room for prospective and declared Senate candidates in the Lone Star State. Texas voters have elected him three times as lieutenant governor, and he can also self-fund his campaign to a significant extent — a key asset in such an expensive state.

He joins a GOP primary that includes former Dallas mayor Tom Leppert and former state solicitor general Ted Cruz, who has gained early tea party support in the race. State Sen. Dan Patrick has also filed paperwork for an exploratory committee.

But early polling has made clear that Dewhurst begins the race as the frontrunner. A University of Texas poll in May showed him way out in front of the GOP field.

The field has changed significantly since then, though, and Leppert and Cruz have both served notice that they will be serious candidates.

On the Democratic side, former Army Gen. Ricardo Sanchez is running but struggled with his early fundraising. And Texas has recently proven a very tough state for Democrats to win statewide.

Jim Bognet, who has worked for former California governor Arnold Schwarzenegger, 2010 California governor candidate Steve Poizner and Mitt Romney’s presidential campaign, will serve as Dewhurst’s campaign manager.