Mr. President, please leave our electoral process alone!

President Obama pushed Massachusetts lawmakers yesterday to rewrite a 2004 election law and allow Governor Deval Patrick to appoint an interim senator to fill Edward M. Kennedy’s Senate seat, casting himself into a tight debate whose outcome, participants said, is largely unknowable.

Meanwhile, Senate President Therese Murray, who has been quiet on the proposal, said after a three-hour Democratic caucus that the heckling Obama received during a congressional address Wednesday might have influenced state legislators to support the temporary appointment, motivated by hopes for federal health care legislation.

Still, Senate and House members said the levels of support for the proposal remained unclear, despite consistent pressure from Washington Democrats that increased yesterday with Obama asking supporters to call their legislators and lobby for the bill’s passage.

Obama’s political operation, Organizing for America, called the empty Massachusetts seat, which would give Senate Democrats a 60th seat and probably prevent a Republican filibuster, “a needed vote in favor of real health reform.’’

“We need to make sure that Governor Patrick can appoint an interim senator until a special election can be held,’’ the group said.

Republicans said Obama’s involvement, after weeks of public neutrality, is proof that Democrats are motivated by politics rather than good government.

UPDATE: From the Globe.

SECOND UPDATE: More from Politico, Boston Herald and the Boston Business Journal.

THIRD UPDATE: From Joan Vennochi.