The District political establishment is in the throes of primary election fever this week. Meanwhile, on Capitol Hill, there could be movement soon on one of the city’s top legislative priorities.

Shadow Sen. Paul Strauss said Thursday that he has secured a commitment from Sen. Mark Begich (D-Alaska) to introduce bills that would grant the city budget autonomy and legislative autonomy from Congress, companions to similar bills already introduced in the House.

The election and new Capitol Hill developments are not wholly unrelated: Strauss is up for reelection Tuesday; he is seeking a third six-year term against self-funded challenger Pete Ross, and has been especially eager recently to highlight his efforts on behalf of the voting rights/statehood cause.

But having the support of Begich — chairman of the Homeland Security and Governmental Affairs subcommittee that would handle the bills — is a significant step toward passing D.C.-focused legislation before the 113th Congress expires. Heather Handyside, a spokeswoman for Begich, said the senator “supports these issues” and “we hope to schedule something soon.”

The clock is ticking: On the House side, the fate of budget autonomy lies in the hands of Rep. Darrel Issa (R-Calif.), the District-friendly Oversight and Government Reform Committee chairman. He is set to relinquish his gavel after the midterm elections later this year, and there are no guarantees that the next chairman will be quite so willing to entertain D.C. autonomy issues. On the Senate side, the Democratic majority is serious jeopardy, meaning Begich may not have his gavel come January.

Have no doubt, getting either budget autonomy or legislative autonomy passed would be a heavy lift, with some Republicans determined to attach policy riders opposed by the District’s local officials. But Begich’s willingness to move fast is a reason to be optimistic, Strauss said.

“We could actually pass these bills,” he said. “Getting them out of conference without poison-pill riders is going to be a challenge, but this is doable.”