If the House/Senate have solid Republican majorities why couldn't Obama be impeached for "high crimes and...?

Misdemeanors"? High C & M is understood by some legal experts to be whatever the House considers that phrase to mean. I am assuming here that the Senate would have 60+ Republicans.

Process

The impeachment process is a two-step procedure. The House of Representatives must first pass by a simple majority articles of impeachment, which constitute the formal allegation or allegations. Upon their passage, the defendant has been "impeached". Next, the Senate tries the accused. In the case of the impeachment of a president, the Chief Justice of the United States presides over the proceedings. For the impeachment of any other official, the Constitution is silent on who shall preside, suggesting that this role falls to the Senate's usual presiding officer. This may include the impeachment of the vice president, although legal theories suggest that allowing a defendant to be the judge in his own case would be a blatant conflict of interest. If the Vice President did not preside over an impeachment (of anyone besides the President), the duties would fall to the President pro tempore of the Senate.

To convict the accused, a two-thirds majority of the senators present is required. Conviction automatically removes the defendant from office. Following conviction, the Senate may vote to further punish the individual by barring him from holding future federal office, elected or appointed. Conviction by the Senate does not bar criminal prosecution. Even after an accused has left office, it is possible to impeach to disqualify the person from future office or from certain emoluments of his prior office (such as a pension). If there is no charge for which a two-thirds majority of the senators present vote "guilty", the defendant is acquitted and no punishment is imposed.

History of Federal Impeachment Proceedings in the United States

Two presidents:

Andrew Johnson, Democrat, was impeached in 1868 after violating the then-newly created Tenure of Office Act. President Johnson was acquitted by the Senate, falling one vote short of the necessary 2/3 needed to remove him from office, voting 35-19 to remove him. The Tenure of Office Act would later be found unconstitutional by the Supreme Court of the United States in dicta.

Bill Clinton, Democrat, was impeached on December 19, 1998, by the House of Representatives on articles charging perjury (specifically, lying to a federal grand jury) by a 228–206 vote, and obstruction of justice by a 221–212 vote. The House rejected other articles. One was a count of perjury in a civil deposition in Paula Jones's sexual harassment lawsuit against Clinton (by a 205–229 vote) and an article which accused Clinton of abuse of power by a 48–285 vote. President Clinton was acquitted by the Senate on February 12, 1999. The Senate vote fell short of the necessary 2/3 needed to remove him from office, voting 45-55 to remove him on obstruction of justice and 50-50 on perjury.